101
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Su K, Zhong Y, Zhang S, Li J, Zou CL, Wang Y, Yan H, Zhu SL. Quantum Interference between Nonidentical Single Particles. PHYSICAL REVIEW LETTERS 2022; 129:093604. [PMID: 36083656 DOI: 10.1103/physrevlett.129.093604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 08/09/2022] [Indexed: 06/15/2023]
Abstract
Quantum interference between identical single particles reveals the intrinsic quantum statistic nature of particles, which could not be interpreted through classical physics. Here, we demonstrate quantum interference between nonidentical bosons using a generalized beam splitter based on a quantum memory. The Hong-Ou-Mandel type interference between single photons and single magnons with high visibility is demonstrated, and the crossover from the bosonic to fermionic quantum statistics is observed by tuning the beam splitter to be non-Hermitian. Moreover, multiparticle interference that simulates the behavior of three fermions by three input photons is realized. Our work extends the understanding of the quantum interference effects and demonstrates a versatile experimental platform for studying and engineering quantum statistics of particles.
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Affiliation(s)
- Keyu Su
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Yi Zhong
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
| | - Shanchao Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Jianfeng Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Chang-Ling Zou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
| | - Yunfei Wang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
- Guangdong Provincial Engineering Technology Research Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
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102
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Chen D, Fröch JE, Ru S, Cai H, Wang N, Adamo G, Scott J, Li F, Zheludev N, Aharonovich I, Gao W. Quantum Interference of Resonance Fluorescence from Germanium-Vacancy Color Centers in Diamond. NANO LETTERS 2022; 22:6306-6312. [PMID: 35913802 DOI: 10.1021/acs.nanolett.2c01959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Resonance fluorescence from a quantum emitter is an ideal source to extract indistinguishable photons. By using the cross-polarization to suppress the laser scattering, we observed resonance fluorescence from GeV color centers in diamond at cryogenic temperature. The Fourier-transform-limited line width emission with T2/2T1 ∼ 0.86 allows for two-photon interference based on single GeV color center. Under pulsed excitation, the separated photons exhibit a Hong-Ou-Mandel quantum interference above classical limit, whereas the continuous-wave excitation leads to a coalescence time window of 1.05 radiative lifetime. In addition, we demonstrated a single-shot readout of spin states with a fidelity of 74%. Our experiments lay down the foundation for building a quantum network with GeV color centers in diamond.
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Affiliation(s)
- Disheng Chen
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - Johannes E Fröch
- School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, New South Wales 2007, Australia
| | - Shihao Ru
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Hongbing Cai
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - Naizhou Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - Giorgio Adamo
- The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - John Scott
- School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, New South Wales 2007, Australia
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Faculty of Science, University of Technology Sydney, Ultimo, New South Wales 2007, Australia
| | - Fuli Li
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Nikolay Zheludev
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
- Optoelectronics Research Centre, University of Southampton, Hampshire, SO17 1BJ, United Kingdom
| | - Igor Aharonovich
- School of Mathematical and Physical Sciences, University of Technology Sydney, Ultimo, New South Wales 2007, Australia
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Faculty of Science, University of Technology Sydney, Ultimo, New South Wales 2007, Australia
| | - Weibo Gao
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
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103
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Sultanov V, Santiago-Cruz T, Chekhova MV. Flat-optics generation of broadband photon pairs with tunable polarization entanglement. OPTICS LETTERS 2022; 47:3872-3875. [PMID: 35913336 DOI: 10.1364/ol.458133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
The concept of "flat optics" is quickly conquering different fields of photonics, but its implementation in quantum optics is still in its infancy. In particular, polarization entanglement, strongly required in quantum photonics, is so far not realized on "flat" platforms. Meanwhile, relaxed phase matching of "flat" nonlinear optical sources enables enormous freedom in tailoring their polarization properties. Here we use this freedom to generate photon pairs with tunable polarization entanglement via spontaneous parametric downconversion (SPDC) in a 400-nm GaP film. By changing the pump polarization, we tune the polarization state of photon pairs from maximally entangled to almost disentangled, which is impossible in a single bulk SPDC source. Polarization entanglement, together with the broadband frequency spectrum, results in an ultranarrow (12 fs) Hong-Ou-Mandel effect and promises extensions to hyperentanglement.
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104
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Afsharnia M, Lyu Z, Pertsch T, Schmidt MA, Saravi S, Setzpfandt F. Spectral tailoring of photon pairs from microstructured suspended-core optical fibers with liquid-filled nanochannels. OPTICS EXPRESS 2022; 30:29680-29693. [PMID: 36299137 DOI: 10.1364/oe.461331] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 06/29/2022] [Indexed: 06/16/2023]
Abstract
We theoretically study the generation of photon pairs via spontaneous four-wave mixing (SFWM) in a liquid-filled microstructured suspended-core optical fiber. We show that it is possible to control the wavelength, group velocity, and bandwidths of the two-photon states. Our proposed fiber structure shows a large number of degrees of freedom to engineer the two-photon state. Here, we focus on the factorable state, which shows no spectral correlation in the two-photon components of the state, and allows the heralding of a single-photon pure state without the need for spectral post-filtering.
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105
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Murray R, Lyons A. Two-photon interference LiDAR imaging. OPTICS EXPRESS 2022; 30:27164-27170. [PMID: 36236893 DOI: 10.1364/oe.461248] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 06/15/2022] [Indexed: 06/16/2023]
Abstract
Optical Coherence Tomography (OCT) is a key 3D imaging technology that provides micron scale depth resolution for bio-imaging. This resolution substantially surpasses what it typically achieved in Light Detection and Ranging (LiDAR) which is often limited to the millimetre scale due to the impulse response of the detection electronics. However, the lack of coherence in LiDAR scenes, arising from mechanical motion for example, make OCT practically infeasible. Here we present a quantum interference inspired approach to LiDAR which achieves OCT depth resolutions without the need for high levels of stability. We demonstrate depth imaging capabilities with an effective impulse response of 70 μm, thereby allowing ranging and multiple reflections to be discerned with much higher resolution than conventional LiDAR approaches. This enhanced resolution opens up avenues for LiDAR in 3D facial recognition, and small feature detection/tracking as well as enhancing the capabilities of more complex time-of-flight methods such as imaging through obscurants and non-line-of-sight imaging.
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106
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Zhou J. Characterization of PT-symmetric quantum interference based on the coupled mode theory. OPTICS EXPRESS 2022; 30:23600-23607. [PMID: 36225036 DOI: 10.1364/oe.458881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 06/07/2022] [Indexed: 06/16/2023]
Abstract
In this paper, we propose a comprehensive quantum theoretical framework to formulate the quantum interference inside the parity-time (PT) symmetric waveguide system which is formed by two coupled optical waveguides with unequal losses. Based on the theory, the expression for the well-known Hong-Ou-Mandel (HOM) dip is derived, which is in an exact agreement with the published results. What's more, a novel one-photon quantum interference phenomenon is predicted according to the model, which suggests a quantum interference process similar to the HOM effect can be observed for the one-photon state, while the other photon is lost due to the waveguide attenuation. Such phenomenon cannot occur in a Hermitian system or in the system formed by the waveguides with equal losses.
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107
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Multi-User Measurement-Device-Independent Quantum Key Distribution Based on GHZ Entangled State. ENTROPY 2022; 24:e24060841. [PMID: 35741561 PMCID: PMC9223234 DOI: 10.3390/e24060841] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Revised: 06/14/2022] [Accepted: 06/16/2022] [Indexed: 11/17/2022]
Abstract
As a multi-particle entangled state, the Greenberger-Horne-Zeilinger (GHZ) state plays an important role in quantum theory and applications. In this study, we propose a flexible multi-user measurement-device-independent quantum key distribution (MDI-QKD) scheme based on a GHZ entangled state. Our scheme can distribute quantum keys among multiple users while being resistant to detection attacks. Our simulation results show that the secure distance between each user and the measurement device can reach more than 280 km while reducing the complexity of the quantum network. Additionally, we propose a method to expand our scheme to a multi-node with multi-user network, which can further enhance the communication distance between the users at different nodes.
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108
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Chapman JC, Peters NA. Heterodyne spectrometer sensitivity limit for quantum networking. APPLIED OPTICS 2022; 61:5002-5009. [PMID: 36256176 DOI: 10.1364/ao.459172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 05/16/2022] [Indexed: 06/16/2023]
Abstract
Optical heterodyne detection-based spectrometers are attractive due to their relatively simple construction and ultrahigh resolution. Here we demonstrate a proof-of-principle single-mode optical-fiber-based heterodyne spectrometer that has picometer resolution and quantum-limited sensitivity around 1550 nm. Moreover, we report a generalized quantum limit of detecting broadband multispectral-temporal-mode light using heterodyne detection, which provides a sensitivity limit on a heterodyne detection-based optical spectrometer. We then compare this sensitivity limit to several spectrometer types and dim light sources of interest such as spontaneous parametric downconversion, Raman scattering, and spontaneous four-wave mixing. We calculate that the heterodyne spectrometer is significantly less sensitive than a single-photon detector and is unable to detect these dim light sources, except for the brightest and narrowest-bandwidth examples.
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109
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Appel MH, Tiranov A, Pabst S, Chan ML, Starup C, Wang Y, Midolo L, Tiurev K, Scholz S, Wieck AD, Ludwig A, Sørensen AS, Lodahl P. Entangling a Hole Spin with a Time-Bin Photon: A Waveguide Approach for Quantum Dot Sources of Multiphoton Entanglement. PHYSICAL REVIEW LETTERS 2022; 128:233602. [PMID: 35749189 DOI: 10.1103/physrevlett.128.233602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Revised: 03/13/2022] [Accepted: 04/06/2022] [Indexed: 06/15/2023]
Abstract
Deterministic sources of multiphoton entanglement are highly attractive for quantum information processing but are challenging to realize experimentally. In this Letter, we demonstrate a route toward a scaleable source of time-bin encoded Greenberger-Horne-Zeilinger and linear cluster states from a solid-state quantum dot embedded in a nanophotonic crystal waveguide. By utilizing a self-stabilizing double-pass interferometer, we measure a spin-photon Bell state with (67.8±0.4)% fidelity and devise steps for significant further improvements. By employing strict resonant excitation, we demonstrate a photon indistinguishability of (95.7±0.8)%, which is conducive to fusion of multiple cluster states for scaling up the technology and producing more general graph states.
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Affiliation(s)
- Martin Hayhurst Appel
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Alexey Tiranov
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Simon Pabst
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Ming Lai Chan
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Christian Starup
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Ying Wang
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Leonardo Midolo
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Konstantin Tiurev
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Sven Scholz
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany
| | - Andreas D Wieck
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany
| | - Arne Ludwig
- Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany
| | - Anders Søndberg Sørensen
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
| | - Peter Lodahl
- Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
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110
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Abstract
This paper presents a theoretical study into the use of optical systems for quantum computation. The study results pertain to quantum sampling and quantum communication and provide a basis for further research and the development of a physical implementation. We propose an optical superstructure that can implement specific computation processes and algorithms. The superstructure is composed of nonlinear optical units, such as beta barium borate crystals. The units are positioned in series, powered by a pulse laser pump, and culminate in a beam splitter that generates the output state of a number of entangled photon pairs. Computation is achieved by entanglement propagation via beam splitters and adjustable phase shifters, which set related parameters. Demonstrating a two-component case, we show how a series of cosine-based components can be implemented. The obtained results open a broad front for future research. Future work should investigate the construction of a quantum optimizer using quantum sampling methods and also investigate high-precision temporal voltage measurement, which is a key procedure for the construction of high-fidelity devices.
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111
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Roiz M, Vainio M. Versatile optical frequency combs based on multi-seeded femtosecond optical parametric generation. OPTICS EXPRESS 2022; 30:17789-17805. [PMID: 36221593 DOI: 10.1364/oe.456763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 04/21/2022] [Indexed: 06/16/2023]
Abstract
This study proposes and demonstrates a versatile method for near- and mid-infrared optical frequency comb generation using multi-seeded femtosecond optical parametric generation. The method allows one to divide the repetition rate by an arbitrarily large integer factor, freely tune the offset frequency, and adjust the common phase offset of the comb modes. Since all possible degrees of freedom are adjustable, the proposed method manifests itself as versatile optical frequency synthesis.
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112
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Gao X, Zhang Y, D'Errico A, Heshami K, Karimi E. High-speed imaging of spatiotemporal correlations in Hong-Ou-Mandel interference. OPTICS EXPRESS 2022; 30:19456-19464. [PMID: 36221721 DOI: 10.1364/oe.456433] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 04/29/2022] [Indexed: 06/16/2023]
Abstract
The Hong-Ou-Mandel interference effect lies at the heart of many emerging quantum technologies whose performance can be significantly enhanced with increasing numbers of entangled modes one could measure and thus utilize. Photon pairs generated through the process of spontaneous parametric down conversion are known to be entangled in a vast number of modes in the various degrees of freedom (DOF) the photons possess such as time, energy, and momentum, etc. Due to limitations in detection technology and techniques, often only one such DOFs can be effectively measured at a time, resulting in much lost potential. Here, we experimentally demonstrate, with the aid of a time tagging camera, high speed measurement and characterization of two-photon interference. With a data acquisition time of only a few seconds, we observe a bi-photon interference and coalescence visibility of ∼64% with potentially up to ∼2 × 103 spatial modes. These results open up a route for practical applications of using the high dimensionality of spatiotemporal DOF in two-photon interference, and in particular, for quantum sensing and communication.
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113
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Lee J, Shen L, Utama AN, Kurtsiefer C. Absolute clock synchronization with a single time-correlated photon pair source over a 10 km optical fibre. OPTICS EXPRESS 2022; 30:18530-18538. [PMID: 36221652 DOI: 10.1364/oe.455542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2022] [Accepted: 04/28/2022] [Indexed: 06/16/2023]
Abstract
We demonstrate a point-to-point clock synchronization protocol based on bidirectionally propagating photons generated in a single spontaneous parametric down-conversion (SPDC) source. Tight timing correlations between photon pairs are used to determine the single and round-trip times measured by two separate clocks, providing sufficient information for distance-independent absolute synchronization secure against symmetric delay attacks. We show that the coincidence signature useful for determining the round-trip time of a synchronization channel, established using a 10 km telecommunications fiber, can be derived from photons reflected off the end face of the fiber without additional optics. Our technique allows the synchronization of multiple clocks with a single reference clock co-located with the source, without requiring additional pair sources, in a client-server configuration suitable for synchronizing a network of clocks.
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114
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Ghosh Dastidar M, Thekkooden I, Nayak PK, Praveen Bhallamudi V. Quantum emitters and detectors based on 2D van der Waals materials. NANOSCALE 2022; 14:5289-5313. [PMID: 35322836 DOI: 10.1039/d1nr08193d] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Light plays an essential role in our world, with several technologies relying on it. Photons will also play an important role in the emerging quantum technologies, which are primed to have a transformative effect on our society. The development of single-photon sources and ultra-sensitive photon detectors is crucial. Solid-state emitters are being heavily pursued for developing truly single-photon sources for scalable technology. On the detectors' side, the main challenge lies in inventing sensitive detectors operating at sub-optical frequencies. This review highlights the promising research being conducted for the development of quantum emitters and detectors based on two-dimensional van der Waals (2D-vdW) materials. Several 2D-vdW materials, from canonical graphene to transition metal dichalcogenides and their heterostructures, have generated a lot of excitement due to their tunable emission and detection properties. The recent developments in the creation, fabrication and control of quantum emitters hosted by 2D-vdW materials and their potential applications in integrated photonic devices are discussed. Furthermore, the progress in enhancing the photon-counting potential of 2D material-based detectors, viz. 2D photodetectors, bolometers and superconducting single-photon detectors functioning at various wavelengths is also reported.
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Affiliation(s)
- Madhura Ghosh Dastidar
- 2D Materials Research and Innovation Group, Micro Nano and Bio-Fluidics Group, Quantum Centers in Diamond and Emerging Materials (QuCenDiEM) Group, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Immanuel Thekkooden
- Quantum Centers in Diamond and Emerging Materials (QuCenDiEM) Group, Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Pramoda K Nayak
- 2D Materials Research and Innovation Group, Micro Nano and Bio-Fluidics Group, Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India.
| | - Vidya Praveen Bhallamudi
- Quantum Centers in Diamond and Emerging Materials (QuCenDiEM) Group, Departments of Physics and Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India.
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115
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Eshun A, Varnavski O, Villabona-Monsalve JP, Burdick RK, Goodson T. Entangled Photon Spectroscopy. Acc Chem Res 2022; 55:991-1003. [PMID: 35312287 DOI: 10.1021/acs.accounts.1c00687] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
The enhanced interest in quantum-related phenomena has provided new opportunities for chemists to push the limits of detection and analysis of chemical processes. As some have called this the second quantum revolution, a time has come to apply the rules learned from previous research in quantum phenomena toward new methods and technologies important to chemists. While there has been great interest recently in quantum information science (QIS), the quest to understand how nonclassical states of light interact with matter has been ongoing for more than two decades. Our entry into this field started around this time with the use of materials to produce nonclassical states of light. Here, the process of multiphoton absorption led to photon-number squeezed states of light, where the photon statistics are sub-Poissonian. In addition to the great interest in generating squeezed states of light, there was also interest in the formation of entangled states of light. While much of the effort is still in foundational physics, there are numerous new avenues as to how quantum entanglement can be applied to spectroscopy, imaging, and sensing. These opportunities could have a large impact on the chemical community for a broad spectrum of applications.In this Account, we discuss the use of entangled (or quantum) light for spectroscopy as well as applications in microscopy and interferometry. The potential benefits of the use of quantum light are discussed in detail. From the first experiments in porphyrin dendrimer systems by Dr. Dong-Ik Lee in our group to the measurements of the entangled two photon absorption cross sections of biological systems such as flavoproteins, the usefulness of entangled light for spectroscopy has been illustrated. These early measurements led the way to more advanced measurements of the unique characteristics of both entangled light and the entangled photon absorption cross-section, which provides new control knobs for manipulating excited states in molecules.The first reports of fluorescence-induced entangled processes were in organic chromophores where the entangled photon cross-section was measured. These results would later have widespread impact in applications such as entangled two-photon microscopy. From our design, construction and implementation of a quantum entangled photon excited microscope, important imaging capabilities were achieved at an unprecedented low excitation intensity of 107 photons/s, which is 6 orders of magnitude lower than the excitation level for the classical two-photon image. New reports have also illustrated an advantage of nonclassical light in Raman imaging as well.From a standpoint of more precise measurements, the use of entangled photons in quantum interferometry may offer new opportunities for chemistry research. Experiments that combine molecular spectroscopy and quantum interferometry, by utilizing the correlations of entangled photons in a Hong-Ou-Mandel (HOM) interferometer, have been carried out. The initial experiment showed that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer. In addition, parameters such as the dephasing time have been obtained with the opportunity for even more advanced phenomenology in the future.
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Affiliation(s)
- Audrey Eshun
- Department of Chemistry, University of Michigan, 930 North UniversityAnn Arbor, Michigan 48103, United States
| | - Oleg Varnavski
- Department of Chemistry, University of Michigan, 930 North UniversityAnn Arbor, Michigan 48103, United States
| | - Juan P. Villabona-Monsalve
- Department of Chemistry, University of Michigan, 930 North UniversityAnn Arbor, Michigan 48103, United States
| | - Ryan K. Burdick
- Department of Chemistry, University of Michigan, 930 North UniversityAnn Arbor, Michigan 48103, United States
| | - Theodore Goodson
- Department of Chemistry, University of Michigan, 930 North UniversityAnn Arbor, Michigan 48103, United States
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116
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Li SL, Yong HL, Li YH, Yang KX, Fu HB, Liu H, Liang H, Ren JG, Cao Y, Yin J, Peng CZ, Pan JW. Experimental demonstration of free-space two-photon interference. OPTICS EXPRESS 2022; 30:11684-11692. [PMID: 35473107 DOI: 10.1364/oe.452267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2021] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
Quantum interference plays an essential role in understanding the concepts of quantum physics. Moreover, the interference of photons is indispensable for large-scale quantum information processing. With the development of quantum networks, interference of photons transmitted through long-distance fiber channels has been widely implemented. However, quantum interference of photons using free-space channels is still scarce, mainly due to atmospheric turbulence. Here, we report an experimental demonstration of Hong-Ou-Mandel interference with photons transmitted by free-space channels. Two typical photon sources, i.e., correlated photon pairs generated in spontaneous parametric down conversion (SPDC) process and weak coherent states, are employed. A visibility of 0.744 ± 0.013 is observed by interfering with two photons generated in the SPDC process, exceeding the classical limit of 0.5. Our results demonstrate that the quantum property of photons remains even after transmission through unstable free-space channels, indicating the feasibility and potential application of free-space-based quantum interference in quantum information processing.
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117
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Koong ZX, Cygorek M, Scerri E, Santana TS, Park SI, Song JD, Gauger EM, Gerardot BD. Coherence in cooperative photon emission from indistinguishable quantum emitters. SCIENCE ADVANCES 2022; 8:eabm8171. [PMID: 35302855 PMCID: PMC8932659 DOI: 10.1126/sciadv.abm8171] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 01/27/2022] [Indexed: 06/14/2023]
Abstract
Photon-mediated interactions between atoms can arise via coupling to a common electromagnetic mode or by quantum interference. Here, we probe the role of coherence in cooperative emission arising from two distant but indistinguishable solid-state emitters because of path erasure. The primary signature of cooperative emission, the emergence of "bunching" at zero delay in an intensity correlation experiment, is used to characterize the indistinguishability of the emitters, their dephasing, and the degree of correlation in the joint system that can be coherently controlled. In a stark departure from a pair of uncorrelated emitters, in Hong-Ou-Mandel-type interference measurements, we observe photon statistics from a pair of indistinguishable emitters resembling that of a weak coherent state from an attenuated laser. Our experiments establish techniques to control and characterize cooperative behavior between matter qubits using the full quantum optics toolbox, a key step toward realizing large-scale quantum photonic networks.
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Affiliation(s)
- Zhe Xian Koong
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Moritz Cygorek
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Eleanor Scerri
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Ted S. Santana
- Centro de Cîencias Naturais e Humanas, Universidade Federal do ABC, Santo Andrè, São Paulo 09210-580, Brazil
| | - Suk In Park
- Center for Opto-Electronic Materials and Devices Research, Korea Institute of Science and Technology, Seoul 02792, Republic of Korea
| | - Jin Dong Song
- Center for Opto-Electronic Materials and Devices Research, Korea Institute of Science and Technology, Seoul 02792, Republic of Korea
| | - Erik M. Gauger
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Brian D. Gerardot
- SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
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118
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Ham BS. Randomness-based macroscopic Franson-type nonlocal correlation. Sci Rep 2022; 12:3759. [PMID: 35260682 PMCID: PMC8904538 DOI: 10.1038/s41598-022-07740-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 02/14/2022] [Indexed: 11/30/2022] Open
Abstract
Franson-type nonlocal correlation is related to Bell inequality violation tests and has been applied for quantum key distributions based on time bin methods. Using unbalanced Mach–Zehnder interferometers, Franson correlation measurements result in an interference fringe, while local measurements do not. Here, randomness-based macroscopic Franson-type correlation is presented using polarization-based two-mode coherent photons, where the quantum correlation is tested by a Hong-Ou-Mandel scheme. Coherent photons are used to investigate the wave properties of this correlation. Without contradicting the wave-particle duality of quantum mechanics, the proposed method provides fundamental understanding of the quantum nature and opens the door to deterministic quantum information science.
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Affiliation(s)
- Byoung S Ham
- School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology, 123 Chumdangwagi-ro, Buk-gu, Gwangju, 61005, South Korea.
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119
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Wang X, Wang J, Ren Z, Wen R, Zou CL, Siviloglou GA, Chen JF. Quantum Interference between Photons and Single Quanta of Stored Atomic Coherence. PHYSICAL REVIEW LETTERS 2022; 128:083605. [PMID: 35275680 DOI: 10.1103/physrevlett.128.083605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2021] [Accepted: 02/07/2022] [Indexed: 06/14/2023]
Abstract
Essential for building quantum networks over remote independent nodes, the indistinguishability of photons has been extensively studied by observing the coincidence dip in the Hong-Ou-Mandel interferometer. However, indistinguishability is not limited to the same type of bosons. For the first time, we hereby observe quantum interference between flying photons and a single quantum of stored atomic coherence (magnon) in an atom-light beam splitter interface. We demonstrate that the Hermiticity of this interface determines the type of quantum interference between photons and magnons. Consequently, not only the bunching behavior that characterizes bosons is observed, but counterintuitively, fermionlike antibunching as well. The hybrid nature of the demonstrated magnon-photon quantum interface can be applied to versatile quantum memory platforms, and can lead to fundamentally different photon distributions from those occurring in boson sampling.
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Affiliation(s)
- Xingchang Wang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy (SIQA), and Shenzhen Branch, Hefei National Laboratory, Futian District, Shenzhen 518055, China
| | - Jianmin Wang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy (SIQA), and Shenzhen Branch, Hefei National Laboratory, Futian District, Shenzhen 518055, China
| | - Zhiqiang Ren
- State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Rong Wen
- Key Laboratory of Advanced Transducers and Intelligent Control System of Ministry of Education, College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
| | - Chang-Ling Zou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, Anhui, China
| | - Georgios A Siviloglou
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy (SIQA), and Shenzhen Branch, Hefei National Laboratory, Futian District, Shenzhen 518055, China
| | - J F Chen
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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120
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Yang C, Zhou ZY, Li Y, Li YH, Niu SJ, Ge Z, Guo GC, Shi BS. Measuring the tuning curve of spontaneous parameter downconversion using a comet-tail-like pattern. OPTICS LETTERS 2022; 47:898-901. [PMID: 35167553 DOI: 10.1364/ol.447674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 01/11/2022] [Indexed: 06/14/2023]
Abstract
Comet-tail-like interference patterns are observed using photons from the spontaneous parametric downconversion (SPDC) process. The patterns are caused by the angular-spectrum-dependent interference and the diffraction of a blazed grating. We present a theoretical explanation and simulation results for these patterns, which are in good agreement with the experimental results. The most significant feature of the patterns is the bright parabolic contour profile, from which one can deduce the parameter of the parabolic tuning curve of the SPDC process. This method could be helpful when designing experiments based on SPDC.
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121
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Feng LT, Zhang M, Xiong X, Liu D, Cheng YJ, Jing FM, Qi XZ, Chen Y, He DY, Guo GP, Guo GC, Dai DX, Ren XF. Transverse Mode-Encoded Quantum Gate on a Silicon Photonic Chip. PHYSICAL REVIEW LETTERS 2022; 128:060501. [PMID: 35213196 DOI: 10.1103/physrevlett.128.060501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
As an important degree of freedom (d.o.f.) in photonic integrated circuits, the orthogonal transverse mode provides a promising and flexible way to increase communication capability, for both classical and quantum information processing. To construct large-scale on-chip multimode multi-d.o.f.s quantum systems, a transverse mode-encoded controlled-NOT (CNOT) gate is necessary. Here, with the help of our new transverse mode-dependent directional coupler and attenuator, we demonstrate the first multimode implementation of a 2-qubit quantum gate. The ability of the gate is demonstrated by entangling two separated transverse mode qubits with an average fidelity of 0.89±0.02 and the achievement of 10 standard deviations of violations in the quantum nonlocality verification. In addition, a fidelity of 0.82±0.01 is obtained from quantum process tomography used to completely characterize the CNOT gate. Our work paves the way for universal transverse mode-encoded quantum operations and large-scale multimode multi-d.o.f.s quantum systems.
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Affiliation(s)
- Lan-Tian Feng
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Ming Zhang
- State Key Laboratory for Modern Optical Instrumentation, Centre for Optical and Electromagnetic Research, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou 310058, China
- Ningbo Research Institute, Zhejiang University, Ningbo 315100, China
| | - Xiao Xiong
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Di Liu
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yu-Jie Cheng
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Fang-Ming Jing
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xiao-Zhuo Qi
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Yang Chen
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - De-Yong He
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guo-Ping Guo
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Dao-Xin Dai
- State Key Laboratory for Modern Optical Instrumentation, Centre for Optical and Electromagnetic Research, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Zijingang Campus, Hangzhou 310058, China
- Ningbo Research Institute, Zhejiang University, Ningbo 315100, China
| | - Xi-Feng Ren
- Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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122
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Asban S, Chernyak VY, Mukamel S. Nonlinear quantum interferometric spectroscopy with entangled photon pairs. J Chem Phys 2022; 156:094202. [DOI: 10.1063/5.0079049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Shahaf Asban
- University of California Irvine Department of Chemistry, United States of America
| | | | - Shaul Mukamel
- Department of Chemistry, University of California Irvine Department of Chemistry, United States of America
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123
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Li Y, Wen Y, Wang S, Liu C, Liu H, Wang M, Sun C, Gao Y, Li S, Wang H. Generation of entanglement between a highly wave-packet-tunable photon and a spin-wave memory in cold atoms. OPTICS EXPRESS 2022; 30:2792-2802. [PMID: 35209412 DOI: 10.1364/oe.446837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
Controls of waveforms (pulse durations) of single photons are important tasks for effectively interconnecting disparate atomic memories in hybrid quantum networks. So far, the waveform control of a single photon that is entangled with an atomic memory remains unexplored. Here, we demonstrated control of waveform length of the photon that is entangled with an atomic spin-wave memory by varying light-atom interaction time in cold atoms. The Bell parameter S as a function of the duration of photon pulse is measured, which shows that violations of Bell inequality can be achieved for the photon pulse in the duration range from 40 ns to 50 µs, where, S = 2.64 ± 0.02 and S = 2.26 ± 0.05 for the 40-ns and 50-µs durations, respectively. The measured results show that S parameter decreases with the increase in the pulse duration. We confirm that the increase in photon noise probability per pulse with the pulse-duration is responsible for the S decrease.
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124
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Zhao W, Huo N, Cui L, Li X, Ou ZY. Propagation of temporal mode multiplexed optical fields in fibers: influence of dispersion. OPTICS EXPRESS 2022; 30:447-459. [PMID: 35201221 DOI: 10.1364/oe.448013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Accepted: 12/15/2021] [Indexed: 06/14/2023]
Abstract
Exploiting two interfering fields which are initially in the same temporal mode but with the spectra altered by propagating through different fibers, we characterize how the spectral profiles of temporal modes change with the fiber induced dispersion by measuring the fourth-order interference when the order number and bandwidth of temporal modes are varied. The experiment is done by launching a pulsed field in different temporal modes into an unbalanced Mach-Zehnder interferometer, in which the fiber lengths in two arms are different. The results show that the mode mismatch of two interfering fields, reflected by the visibility and pattern of interference, is not only dependent upon the amount of unbalanced dispersion but also related to the order number of temporal mode. In particular, the two interfering fields may become orthogonal under a modest amount of unbalanced dispersion when the mode number of the fields is k ≥ 2. Moreover, we discuss how to recover the spectrally distorted temporal mode by measuring and compensating the transmission induced dispersion. Our investigation paves the way for further investigating the distribution of temporally multiplexed quantum states in fiber network.
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125
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Quantum Entanglement of Monochromatic and Non-Monochromatic Photons on a Waveguide Beam Splitter. ENTROPY 2021; 24:e24010049. [PMID: 35052075 PMCID: PMC8775046 DOI: 10.3390/e24010049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 12/21/2021] [Accepted: 12/24/2021] [Indexed: 11/16/2022]
Abstract
It is well known that the waveguide beam splitter can be used as a source for the quantum entanglement of photons. The analysis of such quantum entanglement is a difficult problem even for monochromatic photons, since the system under study is multiparametric. This paper will show that quantum entanglement can be represented in a simple form not only for monochromatic photons but also for non-monochromatic ones. It will be shown that quantum entanglement for non-monochromatic photons can be very different from monochromatic photons, which can be used to create large quantum entanglement.
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126
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Hiekkamäki M, Bouchard F, Fickler R. Photonic Angular Superresolution Using Twisted N00N States. PHYSICAL REVIEW LETTERS 2021; 127:263601. [PMID: 35029483 DOI: 10.1103/physrevlett.127.263601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Revised: 10/01/2021] [Accepted: 11/16/2021] [Indexed: 06/14/2023]
Abstract
The increased phase sensitivity of N00N states has been used in many experiments, often involving photon paths or polarization. Here we experimentally combine the phase sensitivity of N00N states with the orbital angular momentum (OAM) of photons up to 100 ℏ, to resolve rotations of a light field around its optical axis. The results show that both a higher photon number and larger OAM increase the resolution and achievable sensitivity. The presented method opens a viable path to unconditional angular supersensitivity and accessible generation of N00N states between any transverse light fields.
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Affiliation(s)
- Markus Hiekkamäki
- Tampere University, Photonics Laboratory, Physics Unit, Tampere FI-33720, Finland
| | - Frédéric Bouchard
- National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Robert Fickler
- Tampere University, Photonics Laboratory, Physics Unit, Tampere FI-33720, Finland
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127
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Gu B, Keefer D, Mukamel S. Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules. J Chem Theory Comput 2021; 18:406-414. [PMID: 34920666 DOI: 10.1021/acs.jctc.1c00949] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.
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Affiliation(s)
- Bing Gu
- Department of Chemistry & Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, United States
| | - Daniel Keefer
- Department of Chemistry & Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, United States
| | - Shaul Mukamel
- Department of Chemistry & Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, United States
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128
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Wu D, Zhao Q, Gu XM, Zhong HS, Zhou Y, Peng LC, Qin J, Luo YH, Chen K, Li L, Liu NL, Lu CY, Pan JW. Robust Self-Testing of Multiparticle Entanglement. PHYSICAL REVIEW LETTERS 2021; 127:230503. [PMID: 34936806 DOI: 10.1103/physrevlett.127.230503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Revised: 09/14/2021] [Accepted: 11/04/2021] [Indexed: 06/14/2023]
Abstract
Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Because of the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multiphoton genuinely entangled quantum states. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.
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Affiliation(s)
- Dian Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Qi Zhao
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Xue-Mei Gu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Han-Sen Zhong
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - You Zhou
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore
| | - Li-Chao Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jian Qin
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Yi-Han Luo
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Kai Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
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129
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Grudka A, Kurzyński P, Wójcik A. Quantum semipermeable barriers: Investigating Maxwell's demon toolbox. Phys Rev E 2021; 104:064114. [PMID: 35030905 DOI: 10.1103/physreve.104.064114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Accepted: 11/24/2021] [Indexed: 06/14/2023]
Abstract
We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilizes an auxiliary system A and we study how properties of A influence the behavior of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless A is infinite. In addition, coherent superpositions and quantum correlations are affected once particles enter the confinement region. Finally, we show that initial superposition of A allows the barrier to act as a beam splitter.
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Affiliation(s)
- Andrzej Grudka
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
| | - Paweł Kurzyński
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
- Centre for Quantum Technologies, National University of Singapore, 117543 Singapore
| | - Antoni Wójcik
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
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130
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Ramos-Israde E, Garay-Palmett K, Cudney RS. Randomly aperiodically poled LiNbO 3 crystal design by Monte Carlo-Metropolis with simulated annealing optimization for ultrabroadband photon pair generation. APPLIED OPTICS 2021; 60:10587-10593. [PMID: 35200920 DOI: 10.1364/ao.438928] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 11/03/2021] [Indexed: 06/14/2023]
Abstract
We report a scheme for generating ultrabroadband two-photon states by spontaneous parametric downconversion (SPDC) using randomly aperiodically poled crystals designed with an optimization algorithm based on the Monte Carlo-Metropolis method with simulated annealing. A particular SPDC source is discussed, showing results of the spectral and temporal properties of the emitted two-photon states, obtaining almost transform-limited SPDC biphoton wave packets. We also analyze the effect of fabrication errors on the SPDC.
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131
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Gu B, Keefer D, Aleotti F, Nenov A, Garavelli M, Mukamel S. Photoisomerization transition state manipulation by entangled two-photon absorption. Proc Natl Acad Sci U S A 2021; 118:e2116868118. [PMID: 34799455 PMCID: PMC8617409 DOI: 10.1073/pnas.2116868118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 10/15/2021] [Indexed: 11/18/2022] Open
Abstract
We demonstrate how two-photon excitation with quantum light can influence elementary photochemical events. The azobenzene trans → cis isomerization following entangled two-photon excitation is simulated using quantum nuclear wave packet dynamics. Photon entanglement modulates the nuclear wave packets by coherently controlling the transition pathways. The photochemical transition state during passage of the reactive conical intersection in azobenzene photoisomerization is strongly affected with a noticeable alteration of the product yield. Quantum entanglement thus provides a novel control knob for photochemical reactions. The distribution of the vibronic coherences during the conical intersection passage strongly depends on the shape of the initial wave packet created upon quantum light excitation. X-ray signals that can experimentally monitor this coherence are simulated.
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Affiliation(s)
- Bing Gu
- Department of Chemistry, University of California, Irvine, CA 92697
- Department of Physics & Astronomy, University of California, Irvine, CA 92697
| | - Daniel Keefer
- Department of Chemistry, University of California, Irvine, CA 92697
- Department of Physics & Astronomy, University of California, Irvine, CA 92697
| | - Flavia Aleotti
- Dipartimento di Chimica Industriale "Toso Montanari", Università degli studi di Bologna, 40136 Bologna, Italy
| | - Artur Nenov
- Dipartimento di Chimica Industriale "Toso Montanari", Università degli studi di Bologna, 40136 Bologna, Italy
| | - Marco Garavelli
- Dipartimento di Chimica Industriale "Toso Montanari", Università degli studi di Bologna, 40136 Bologna, Italy
| | - Shaul Mukamel
- Department of Chemistry, University of California, Irvine, CA 92697;
- Department of Physics & Astronomy, University of California, Irvine, CA 92697
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132
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Shringarpure SU, Franson JD. Proposal for a destructive controlled phase gate using linear optics. Sci Rep 2021; 11:22067. [PMID: 34764334 PMCID: PMC8586020 DOI: 10.1038/s41598-021-01384-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 10/13/2021] [Indexed: 11/09/2022] Open
Abstract
Knill, Laflamme, and Milburn showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate for a single-rail target qubit that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-phase gate destroys the control qubit, which is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process.
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Affiliation(s)
- S U Shringarpure
- Physics Department, University of Maryland Baltimore County, Baltimore, MD, 21250, USA.
| | - J D Franson
- Physics Department, University of Maryland Baltimore County, Baltimore, MD, 21250, USA
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133
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Tsujimoto Y, Wakui K, Fujiwara M, Sasaki M, Takeoka M. Ultra-fast Hong-Ou-Mandel interferometry via temporal filtering. OPTICS EXPRESS 2021; 29:37150-37160. [PMID: 34808793 DOI: 10.1364/oe.430502] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
Heralded single photons (HSPs) generated by spontaneous parametric down-conversion (SPDC) are useful resource to achieve various photonic quantum information processing. Given a large-scale experiment which needs multiple HSPs, increasing the generation rate with suppressing higher-order pair creation is desirable. One of the promising ways is to use a pump laser with a GHz-order repetition rate. In such a high repetition rate regime, however, single-photon detectors can only partially identify the pulses. Hence, we develop a simple model to consider that effect on the spectral purity, and experimentally demonstrate a high-visibility Hong-Ou-Mandel interference between two independent HSPs generated by SPDC with 3.2 GHz-repetition-rate mode-locked pump pulses. The observed visibility of 0.88(3) is in good agreement with our theoretical model.
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134
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Keramati S, Brunner W, Gay TJ, Batelaan H. Non-Poissonian Ultrashort Nanoscale Electron Pulses. PHYSICAL REVIEW LETTERS 2021; 127:180602. [PMID: 34767409 DOI: 10.1103/physrevlett.127.180602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Revised: 09/09/2021] [Accepted: 09/28/2021] [Indexed: 05/12/2023]
Abstract
The statistical character of electron beams used in current technologies, as described by a stream of particles, is random in nature. Using coincidence measurements of femtosecond pulsed electron pairs, we report the observation of sub-Poissonian electron statistics that are nonrandom due to two-electron Coulomb interactions, and that exhibit an antibunching signal of 1 part in 4. This advancement is a fundamental step toward observing a strongly quantum degenerate electron beam needed for many applications, and in particular electron correlation spectroscopy.
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Affiliation(s)
- Sam Keramati
- Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
| | - Will Brunner
- Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
| | - T J Gay
- Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
| | - Herman Batelaan
- Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
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135
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Conflict-free collective stochastic decision making by orbital angular momentum of photons through quantum interference. Sci Rep 2021; 11:21117. [PMID: 34702905 PMCID: PMC8548474 DOI: 10.1038/s41598-021-00493-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Accepted: 10/12/2021] [Indexed: 11/09/2022] Open
Abstract
In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here we propose a scalable principle to solve competitive decision-making situations by using the orbital angular momentum of photons based on its high dimensionality, which theoretically allows an unlimited number of arms. Moreover, by extending the Hong-Ou-Mandel effect to more than two states, we theoretically establish an experimental configuration able to generate multi-photon states with orbital angular momentum and conditions that provide conflict-free selections at every turn. We numerically examine total rewards regarding three-armed bandit problems, for which the proposed strategy accomplishes almost the theoretical maximum, which is greater than a conventional mixed strategy intending to realize Nash equilibrium. This is thanks to the quantum interference effect that achieves no-conflict selections, even in the exploring phase to find the best arms.
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136
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Yang C, Zhou ZY, Li Y, Liu SK, Ge Z, Guo GC, Shi BS. Angular-spectrum-dependent interference. LIGHT, SCIENCE & APPLICATIONS 2021; 10:217. [PMID: 34702833 PMCID: PMC8548309 DOI: 10.1038/s41377-021-00661-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Revised: 09/30/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
Optical interference is not only a fundamental phenomenon that has enabled new theories of light to be derived but it has also been used in interferometry for the measurement of small displacements, refractive index changes, and surface irregularities. In a two-beam interferometer, variations in the interference fringes are used as a diagnostic for anything that causes the optical path difference (OPD) to change; therefore, for a specified OPD, greater variation in the fringes indicates better measurement sensitivity. Here, we introduce and experimentally validate an interesting optical interference phenomenon that uses photons with a structured frequency-angular spectrum, which are generated from a spontaneous parametric down-conversion process in a nonlinear crystal. This interference phenomenon is manifested as interference fringes that vary much more rapidly with increasing OPD than the corresponding fringes for equal-inclination interference; the phenomenon is parameterised using an equivalent wavelength, which under our experimental conditions is 29.38 nm or about 1/27 of the real wavelength. This phenomenon not only enriches the knowledge with regard to optical interference but also offers promise for applications in interferometry.
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Grants
- 61605194, 61435011, 61525504 National Natural Science Foundation of China (National Science Foundation of China)
- 61605194, 61435011, 61525504 National Natural Science Foundation of China (National Science Foundation of China)
- 61605194, 61435011, 61525504 National Natural Science Foundation of China (National Science Foundation of China)
- 61605194, 61435011, 61525504 National Natural Science Foundation of China (National Science Foundation of China)
- 61605194, 61435011, 61525504 National Natural Science Foundation of China (National Science Foundation of China)
- Anhui Initiative In Quantum Information Technologies (AHY020200)
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Affiliation(s)
- Chen Yang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Zhi-Yuan Zhou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, China.
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China.
| | - Yan Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Shi-Kai Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Zheng Ge
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, China
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China
| | - Bao-Sen Shi
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui, China.
- Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science and Technology of China, Hefei, Anhui, China.
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137
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Lipka M, Parniak M. Single-Photon Hologram of a Zero-Area Pulse. PHYSICAL REVIEW LETTERS 2021; 127:163601. [PMID: 34723616 DOI: 10.1103/physrevlett.127.163601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 09/17/2021] [Indexed: 06/13/2023]
Abstract
Single photons exhibit inherently quantum and unintuitive properties such as the Hong-Ou-Mandel effect, demonstrating their bosonic and quantized nature, yet at the same time may correspond to single excitations of spatial or temporal modes with a very complex structure. Those two features are rarely seen together. Here we experimentally demonstrate how the Hong-Ou-Mandel effect can be spectrally resolved and harnessed to characterize a complex temporal mode of a single-photon-a zero-area pulse-obtained via a resonant interaction of a terahertz-bandwidth photon with a narrow gigahertz-wide atomic transition of atomic vapor. The combination of bosonic quantum behavior with bandwidth-mismatched light-atom interaction is of fundamental importance for deeper understanding of both phenomena, as well as their engineering offering applications in characterization of ultrafast transient processes.
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Affiliation(s)
- Michał Lipka
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Michał Parniak
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
- Niels Bohr Institute, University of Copanhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark
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138
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Abstract
Multiphoton interference is an important phenomenon in modern quantum mechanics and experimental quantum optics, and it is fundamental for the development of quantum information science and technologies. Over the last three decades, several theoretical and experimental studies have been performed to understand the essential principles underlying such interference and to explore potential applications. Recently, the two-photon interference (TPI) of phase-randomized weak coherent states has played a key role in the realization of long-distance quantum communication based on the use of classical light sources. In this context, we investigated TPI experiments with weak coherent pulses at the single-photon level and quantitatively analyzed the results in terms of the single- and coincidence-counting rates and one- and two-photon interference-fringe shapes. We experimentally examined the Hong–Ou–Mandel-type TPI of phase-randomized weak coherent pulses to compare the TPI effect with that of correlated photons. Further experiments were also performed with two temporally- and spatially separated weak coherent pulses. Although the observed interference results, including the results of visibility and fringe shape, can be suitably explained by classical intensity correlation, the physics underlying the TPI effect needs to be interpreted as the interference between the two-photon states at the single-photon level within the utilized interferometer. The results of this study can provide a more comprehensive understanding of the TPI of coherent light at the single-photon level.
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139
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Gebhart V, Pezzè L, Smerzi A. Genuine Multipartite Nonlocality with Causal-Diagram Postselection. PHYSICAL REVIEW LETTERS 2021; 127:140401. [PMID: 34652187 DOI: 10.1103/physrevlett.127.140401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Accepted: 09/02/2021] [Indexed: 06/13/2023]
Abstract
The generation and verification of genuine multipartite nonlocality (GMN) is of central interest for both fundamental research and quantum technological applications, such as quantum privacy. To demonstrate GMN in measurement data, the statistics are commonly postselected by neglecting undesired data. Until now, valid postselection strategies have been restricted to local postselection. A general postselection that is decided after communication between parties can mimic nonlocality, even though the complete data are local. Here, we establish conditions under which GMN is demonstrable even if observations are postselected collectively. Intriguingly, certain postselection strategies that require communication among several parties still offer a demonstration of GMN shared between all parties. The results are derived using the causal structure of the experiment and the no-signaling condition imposed by relativity. Finally, we apply our results to show that genuine three-partite nonlocality can be created with independent particle sources.
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Affiliation(s)
- Valentin Gebhart
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
- Università degli Studi di Napoli "Federico II", Via Cinthia 21, 80126 Napoli, Italy
| | - Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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140
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Ham BS. Macroscopic and deterministic quantum feature generation via phase basis quantization in a cascaded interferometric system. Sci Rep 2021; 11:19058. [PMID: 34561490 PMCID: PMC8463619 DOI: 10.1038/s41598-021-98478-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 09/02/2021] [Indexed: 11/09/2022] Open
Abstract
Quantum entanglement is the quintessence of quantum information science governed by quantum superposition mostly limited to a microscopic regime. For practical applications, however, macroscopic entanglement has an essential benefit for quantum sensing and metrology to beat its classical counterpart. Recently, a coherence approach for entanglement generation has been proposed and demonstrated in a coupled interferometric system using classical laser light, where the quantum feature of entanglement has been achieved via phase basis superposition between identical interferometric systems. Such a coherence method is based on the wave nature of a photon without violating quantum mechanics under the complementarity theory. Here, a method of phase basis quantization via phase basis superposition is presented for macroscopic entanglement in an interferometric system, which is corresponding to the energy quantization of a photon.
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Affiliation(s)
- Byoung S Ham
- School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology, 123 Chumdangwagi-ro, Buk-gu, Gwangju, 61005, South Korea.
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141
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Asban S, Mukamel S. Distinguishability and "which pathway" information in multidimensional interferometric spectroscopy with a single entangled photon-pair. SCIENCE ADVANCES 2021; 7:eabj4566. [PMID: 34550740 PMCID: PMC8457662 DOI: 10.1126/sciadv.abj4566] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Accepted: 08/02/2021] [Indexed: 06/04/2023]
Abstract
Correlated photons inspire abundance of metrology-related platforms, which benefit from quantum (anti-) correlations and outperform their classical counterparts. While these mainly focus on entanglement, the role of photon exchange phase and degree of distinguishability has not been widely used in quantum applications. Using an interferometric setup, we theoretically show that, when a two-photon wave function is coupled to matter, it is encoded with “which pathway?” information even at low-degree of entanglement. An interferometric protocol, which enables phase-sensitive discrimination between microscopic interaction histories (pathways), is developed. We find that quantum light interferometry facilitates utterly different set of time delay variables, which are unbound by uncertainty to the inverse bandwidth of the wave packet. We illustrate our findings on an exciton model system and demonstrate how to probe intraband dephasing in the time domain without temporally resolved detection. The unusual scaling of multiphoton coincidence signals with the applied pump intensity is discussed.
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142
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Cosacchi M, Seidelmann T, Cygorek M, Vagov A, Reiter DE, Axt VM. Accuracy of the Quantum Regression Theorem for Photon Emission from a Quantum Dot. PHYSICAL REVIEW LETTERS 2021; 127:100402. [PMID: 34533331 DOI: 10.1103/physrevlett.127.100402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 08/03/2021] [Indexed: 06/13/2023]
Abstract
The quantum regression theorem (QRT) is the most widely used tool for calculating multitime correlation functions for the assessment of quantum emitters. It is an approximate method based on a Markov assumption for environmental coupling. In this Letter we quantify properties of photons emitted from a single quantum dot coupled to phonons. For the single-photon purity and the indistinguishability, we compare numerically exact path-integral results with those obtained from the QRT. It is demonstrated that the QRT systematically overestimates the influence of the environment for typical quantum dots used in quantum information technology.
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Affiliation(s)
- M Cosacchi
- Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany
| | - T Seidelmann
- Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany
| | - M Cygorek
- Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - A Vagov
- Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany
- ITMO University, St. Petersburg 197101, Russia
| | - D E Reiter
- Institut für Festkörpertheorie, Universität Münster, 48149 Münster, Germany
| | - V M Axt
- Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany
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143
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Ye M, Wang Y, Gao P, Xu L, Huang G. Experimental Hong-Ou-Mandel interference using two independent heralded single-photon sources. FRONTIERS OF OPTOELECTRONICS 2021; 14:360-364. [PMID: 36637726 PMCID: PMC9743834 DOI: 10.1007/s12200-020-0986-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Accepted: 12/10/2019] [Indexed: 06/17/2023]
Abstract
Hong-Ou-Mandel (HOM) interference is one of the most important experimental phenomena in quantum optics. It has drawn considerable attention with respect to quantum cryptography and quantum communication because of the advent of the measurement device independent (MDI) quantum key distribution (QKD) protocol. Here, we realize HOM interference, having a visibility of approximately 38.1%, using two independent heralded single-photon sources (HSPSs). The HOM interference between two independent HSPSs is a core technology for realizing the long-distance MDI QKD protocol, the quantum coin-tossing protocol, and other quantum cryptography protocols.
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Affiliation(s)
- Meng Ye
- CSG Power Generation Company Information Communication Branch, Guangzhou, 510070 China
| | - Yong Wang
- CSG Power Generation Company Information Communication Branch, Guangzhou, 510070 China
| | - Peng Gao
- CSG Power Generation Company Information Communication Branch, Guangzhou, 510070 China
| | - Likun Xu
- CSG Power Generation Company Information Communication Branch, Guangzhou, 510070 China
| | - Guanjin Huang
- CSG Power Generation Company Information Communication Branch, Guangzhou, 510070 China
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144
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Hong S, Ur Rehman J, Kim YS, Cho YW, Lee SW, Jung H, Moon S, Han SW, Lim HT. Quantum enhanced multiple-phase estimation with multi-mode N00N states. Nat Commun 2021; 12:5211. [PMID: 34471118 PMCID: PMC8410777 DOI: 10.1038/s41467-021-25451-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 08/11/2021] [Indexed: 02/07/2023] Open
Abstract
Quantum metrology can achieve enhanced sensitivity for estimating unknown parameters beyond the standard quantum limit. Recently, multiple-phase estimation exploiting quantum resources has attracted intensive interest for its applications in quantum imaging and sensor networks. For multiple-phase estimation, the amount of enhanced sensitivity is dependent on quantum probe states, and multi-mode N00N states are known to be a key resource for this. However, its experimental demonstration has been missing so far since generating such states is highly challenging. Here, we report generation of multi-mode N00N states and experimental demonstration of quantum enhanced multiple-phase estimation using the multi-mode N00N states. In particular, we show that the quantum Cramer-Rao bound can be saturated using our two-photon four-mode N00N state and measurement scheme using a 4 × 4 multi-mode beam splitter. Our multiple-phase estimation strategy provides a faithful platform to investigate multiple parameter estimation scenarios.
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Affiliation(s)
- Seongjin Hong
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Junaid Ur Rehman
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin, Korea
| | - Yong-Su Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Young-Wook Cho
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Department of Physics, Yonsei University, Seoul, Korea
| | - Seung-Woo Lee
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Hojoong Jung
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Sung Moon
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Sang-Wook Han
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Hyang-Tag Lim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea.
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea.
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145
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Kim I, Lee D, Hong S, Cho YW, Jo Lee K, Kim YS, Lim HT. Implementation of a 3 × 3 directionally-unbiased linear optical multiport. OPTICS EXPRESS 2021; 29:29527-29540. [PMID: 34615061 DOI: 10.1364/oe.436075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 08/20/2021] [Indexed: 06/13/2023]
Abstract
Linear optical multiports are widely used in photonic quantum information processing. Naturally, these devices are directionally-biased since photons always propagate from the input ports toward the output ports. Recently, the concept of directionally-unbiased linear optical multiports was proposed. These directionally-unbiased multiports allow photons to propagate along a reverse direction, which can greatly reduce the number of required linear optical elements for complicated linear optical quantum networks. Here, we report an experimental demonstration of a 3 × 3 directionally-unbiased linear optical fiber multiport using an optical tritter and mirrors. Compared to the previous demonstration using bulk optical elements which works only with light sources with a long coherence length, our experimental directionally-unbiased 3 × 3 optical multiport does not require a long coherence length since it provides negligible optical path length differences among all possible optical trajectories. It can be a useful building block for implementing large-scale quantum walks on complex graph networks.
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146
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Zhang Y, England D, Nomerotski A, Sussman B. High speed imaging of spectral-temporal correlations in Hong-Ou-Mandel interference. OPTICS EXPRESS 2021; 29:28217-28227. [PMID: 34614958 DOI: 10.1364/oe.432191] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 07/17/2021] [Indexed: 06/13/2023]
Abstract
In this work we demonstrate spectral-temporal correlation measurements of the Hong-Ou-Mandel (HOM) interference effect with the use of a spectrometer based on a photon-counting camera. This setup allows us to take, within seconds, spectral temporal correlation measurements on entangled photon sources with sub-nanometer spectral resolution and nanosecond timing resolution. Through post processing, we can observe the HOM behaviour for any number of spectral filters of any shape and width at any wavelength over the observable spectral range. Our setup also offers great versatility in that it is capable of operating at a wide spectral range from the visible to the near infrared and does not require a pulsed pump laser for timing purposes. This work offers the ability to gain large amounts of spectral and temporal information from a HOM interferometer quickly and efficiently and will be a very useful tool for many quantum technology applications and fundamental quantum optics research.
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147
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Chen C, Shapiro JH, Wong FNC. Experimental Demonstration of Conjugate-Franson Interferometry. PHYSICAL REVIEW LETTERS 2021; 127:093603. [PMID: 34506171 DOI: 10.1103/physrevlett.127.093603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 08/04/2021] [Indexed: 06/13/2023]
Abstract
Franson interferometry is a well-known quantum measurement technique for probing photon-pair frequency correlations that is often used to certify time-energy entanglement. We demonstrate, for the first time, the complementary technique in the time basis called conjugate-Franson interferometry. It measures photon-pair arrival-time correlations, thus providing a valuable addition to the quantum toolbox. We obtain a conjugate-Franson interference visibility of 96±1% without background subtraction for entangled photon pairs generated by spontaneous parametric down-conversion. Our measured result surpasses the quantum-classical threshold by 25 standard deviations and validates the conjugate-Franson interferometer (CFI) as an alternative method for certifying time-energy entanglement. Moreover, the CFI visibility is a function of the biphoton's joint temporal intensity, and is therefore sensitive to that state's spectral phase variation: something that is not the case for Franson interferometry or Hong-Ou-Mandel interferometry. We highlight the CFI's utility by measuring its visibilities for two different biphoton states: one without and the other with spectral phase variation, observing a 21% reduction in the CFI visibility for the latter. The CFI is potentially useful for applications in areas of photonic entanglement, quantum communications, and quantum networking.
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Affiliation(s)
- Changchen Chen
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jeffrey H Shapiro
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Franco N C Wong
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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148
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Zhang A, Zhan H, Liao J, Zheng K, Jiang T, Mi M, Yao P, Zhang L. Quantum verification of NP problems with single photons and linear optics. LIGHT, SCIENCE & APPLICATIONS 2021; 10:169. [PMID: 34408129 PMCID: PMC8373877 DOI: 10.1038/s41377-021-00608-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Revised: 07/22/2021] [Accepted: 07/30/2021] [Indexed: 06/13/2023]
Abstract
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the satisfiability of potentially conflict constraints (SAT). According to the well-founded exponential time hypothesis, verifying an SAT instance of size n requires generally the complete solution in an O(n)-bit proof. In contrast, quantum verification algorithms, which encode the solution into quantum bits rather than classical bit strings, can perform the verification task with quadratically reduced information about the solution in [Formula: see text] qubits. Here we realize the quantum verification machine of SAT with single photons and linear optics. By using tunable optical setups, we efficiently verify satisfiable and unsatisfiable SAT instances and achieve a clear completeness-soundness gap even in the presence of experimental imperfections. The protocol requires only unentangled photons, linear operations on multiple modes and at most two-photon joint measurements. These features make the protocol suitable for photonic realization and scalable to large problem sizes with the advances in high-dimensional quantum information manipulation and large scale linear-optical systems. Our results open an essentially new route toward quantum advantages and extend the computational capability of optical quantum computing.
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Grants
- National Natural Science Foundation of China (National Science Foundation of China)
- the National Key Research and Development Program of China (Grant Nos. 2019YFA0308700, 2017YFA0303703 and 2018YFB1003202), the National Natural Science Foundation of China (Grant Nos. 61972191, 11690032, 61975077 and 91836303) and the Fundamental Research Funds for the Central Universities (Grant No. 020214380068)
- the National Key Research and Development Program of China (Grant Nos. 2019YFA0308700, 2017YFA0303703 and 2018YFB1003202), the National Natural Science Foundation of China (Grant Nos. 61972191, 11690032, 61975077 and 91836303) and the Fundamental Research Funds for the Central Universities (Grant No. 020214380068).
- the National Key Research and Development Program of China (Grant Nos. 2019YFA0308700, 2017YFA0303703 and 2018YFB1003202), the National Natural Science Foundation of China (Grant Nos. 61972191, 11690032, 61975077 and 91836303) and the Fundamental Research Funds for the Central Universities (Grant No. 020214380068). Anhui Initiative in Quantum Information Technologies (Grant No. AHY150100).
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Affiliation(s)
- Aonan Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Hao Zhan
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Junjie Liao
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Kaimin Zheng
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Tao Jiang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Minghao Mi
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
| | - Penghui Yao
- State Key Laboratory for Novel Software Technology, Nanjing University, 210093, Nanjing, China.
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education) and College of Engineering and Applied Sciences, Nanjing University, 210093, Nanjing, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China.
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149
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Fujihashi Y, Ishizaki A. Achieving two-dimensional optical spectroscopy with temporal and spectral resolution using quantum entangled three photons. J Chem Phys 2021; 155:044101. [PMID: 34340393 DOI: 10.1063/5.0056808] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Recent advances in techniques for generating quantum light have stimulated research on novel spectroscopic measurements using quantum entangled photons. One such spectroscopy technique utilizes non-classical correlations among entangled photons to enable measurements with enhanced sensitivity and selectivity. Here, we investigate the spectroscopic measurement utilizing entangled three photons. In this measurement, time-resolved entangled photon spectroscopy with monochromatic pumping [A. Ishizaki, J. Chem. Phys. 153, 051102 (2020)] is integrated with the frequency-dispersed two-photon counting technique, which suppresses undesired accidental photon counts in the detector and thus allows one to separate the weak desired signal. This time-resolved frequency-dispersed two-photon counting signal, which is a function of two frequencies, is shown to provide the same information as that of coherent two-dimensional optical spectra. The spectral distribution of the phase-matching function works as a frequency filter to selectively resolve a specific region of the two-dimensional spectra, whereas the excited-state dynamics under investigation are temporally resolved in the time region longer than the entanglement time. The signal is not subject to Fourier limitations on the joint temporal and spectral resolution, and therefore, it is expected to be useful for investigating complex molecular systems in which multiple electronic states are present within a narrow energy range.
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Affiliation(s)
- Yuta Fujihashi
- Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585, Japan
| | - Akihito Ishizaki
- Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585, Japan
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150
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Prakash V, Sierant A, Mitchell MW. Autoheterodyne Characterization of Narrow-Band Photon Pairs. PHYSICAL REVIEW LETTERS 2021; 127:043601. [PMID: 34355946 DOI: 10.1103/physrevlett.127.043601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 06/10/2021] [Indexed: 06/13/2023]
Abstract
We describe a technique to measure photon pair joint spectra by detecting the time-correlation beat note when nondegenerate photon pairs interfere at a beam splitter. The technique implements a temporal analog of the Ghosh-Mandel effect with one photon counter and a time-resolved Hong-Ou-Mandel interference with two. It is well suited to characterize pairs of photons, each of which can interact with a single atomic species, as required to study recently predicted photon-photon interaction in subwavelength atomic arrays. With this technique, we characterize photon pairs from cavity-enhanced parametric down-conversion with a bandwidth ≈ 5 MHz and frequency separation of ∼200 MHz near the D_{1} line of atomic Rb.
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Affiliation(s)
- Vindhiya Prakash
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Aleksandra Sierant
- Institute of Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Morgan W Mitchell
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
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