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Liu X, Cao Q, Zhang N, Chong A, Cai Y, Zhan Q. Spatiotemporal optical vortices with controllable radial and azimuthal quantum numbers. Nat Commun 2024; 15:5435. [PMID: 38937504 PMCID: PMC11211508 DOI: 10.1038/s41467-024-49819-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2024] [Accepted: 06/16/2024] [Indexed: 06/29/2024] Open
Abstract
Optical spatiotemporal vortices with transverse photon orbital angular momentum (OAM) have recently become a focal point of research. In this work we theoretically and experimentally investigate optical spatiotemporal vortices with radial and azimuthal quantum numbers, known as spatiotemporal Laguerre-Gaussian (STLG) wavepackets. These 3D wavepackets exhibit phase singularities and cylinder-shaped edge dislocations, resulting in a multi-ring topology in its spatiotemporal profile. Unlike conventional ST optical vortices, STLG wavepackets with non-zero p and l values carry a composite transverse OAM consisting of two directionally opposite components. We further demonstrate mode conversion between an STLG wavepacket and an ST Hermite-Gaussian (STHG) wavepacket through the application of strong spatiotemporal astigmatism. The converted STHG wavepacket is de-coupled in intensity in space-time domain that can be utilized to implement the efficient and accurate recognition of ultrafast STLG wavepackets carried various p and l . This study may offer new insights into high-dimensional quantum information, photonic topology, and nonlinear optics, while promising potential applications in other wave phenomena such as acoustics and electron waves.
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Affiliation(s)
- Xin Liu
- Shandong Provincial Engineering and Technical Center of Light Manipulations and Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan, China
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan, China
| | - Qian Cao
- School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, China
- Zhangjiang Laboratory, Shanghai, China
| | - Nianjia Zhang
- School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, China
| | - Andy Chong
- Department of Physics, Pusan National University, Busan, Republic of Korea
- Institute for Future Earth, Pusan National University, Busan, Republic of Korea
| | - Yangjian Cai
- Shandong Provincial Engineering and Technical Center of Light Manipulations and Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan, China.
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan, China.
| | - Qiwen Zhan
- School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, China.
- Zhangjiang Laboratory, Shanghai, China.
- Westlake Institute for Optoelectronics, Fuyang, Hangzhou, China.
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2
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Liu S, Lv Y, Wang X, Wang J, Lou Y, Jing J. Deterministic All-Optical Quantum Teleportation of Four Degrees of Freedom. PHYSICAL REVIEW LETTERS 2024; 132:100801. [PMID: 38518346 DOI: 10.1103/physrevlett.132.100801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Accepted: 02/02/2024] [Indexed: 03/24/2024]
Abstract
Quantum teleportation, disembodied transfer of the unknown quantum state between two locations, has been experimentally demonstrated for both discrete and continuous variable states in one degree of freedom (DOF). Generally, multiple DOFs are needed to fully characterize a quantum state. Therefore, to implement intact quantum teleportation, multiple DOFs of quantum state should be teleported simultaneously. Recently, teleporting a single photon encoded in two DOFs has been experimentally demonstrated in discrete variable regime. However, the teleportation of more than two DOFs remains unexplored. Here, by utilizing continuous variable hyperentanglement in four DOFs (azimuthal and radial indexes of Laguerre-Gaussian mode, frequency, and polarization), we experimentally demonstrate deterministic all-optical quantum teleportation of four DOFs. Moreover, we experimentally construct 24 parallel teleportation channels. Our results pave the way for deterministically implementing multiple-DOF quantum communication protocols.
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Affiliation(s)
- Shengshuai Liu
- State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yinghui Lv
- State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Xutong Wang
- State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Jiabin Wang
- State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Yanbo Lou
- State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
| | - Jietai Jing
- State Key Laboratory of Precision Spectroscopy, Joint Institute of Advanced Science and Technology, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China
- CAS Center for Excellence in Ultra-intense Laser Science, Shanghai 201800, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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3
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Li H, Li J, Wei D. Conversion and selection of Laguerre-Gaussian modes via a variable aperture in a geometric-phase-plate-assisted optical resonator. OPTICS LETTERS 2023; 48:2672-2675. [PMID: 37186737 DOI: 10.1364/ol.487104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
We numerically analyze the conversion and selection of intracavity modes in a two-mirror optical resonator, which is assisted by a geometric phase plate (GPP) and a circular aperture, along with its output performance of high-order Laguerre-Gaussian (LG) modes. Based on the iterative Fox-Li method and the analysis of modal decomposition, transmission losses, and spot sizes, we find that various self-consistent two-faced resonator modes could be formed by fixing the GPP but changing the size of aperture. Such a feature not only enriches transverse-mode structures inside the optical resonator, but also provides a flexible way to directly output high-purity LG modes for high-capacity optical communication, high-precision interferometers, high-dimensional quantum correlation, etc.
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4
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Guo Z, Chang Z, Zhang Y, Ma G, Zhu X, Jia J, Zhang P. Radial-mode sensitive probe beam in the rotational Doppler effect. OPTICS EXPRESS 2023; 31:7632-7642. [PMID: 36859891 DOI: 10.1364/oe.482431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
The rotational Doppler effect (RDE) attracts much attention in various research areas, from acoustics to optics. The observation of RDE mostly depends on the orbital angular momentum of the probe beam, while the impression of radial mode is ambiguous. To clarify the role of radial modes in RDE detection, we reveal the mechanism of interaction between probe beams and rotating objects based on complete Laguerre-Gaussian (LG) modes. It is theoretically and experimentally proved that radial LG modes play a crucial role in RDE observation because of topological spectroscopic orthogonality between probe beams and objects. We enhance the probe beam by employing multiple radial LG modes, which makes the RDE detection sensitive to objects containing complicated radial structures. In addition, a specific method to estimate the efficiency of various probe beams is proposed. This work has the potential to modify RDE detection method and take the related applications to a new platform.
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5
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Zhang J, Ma J, Parry M, Cai M, Camacho-Morales R, Xu L, Neshev DN, Sukhorukov AA. Spatially entangled photon pairs from lithium niobate nonlocal metasurfaces. SCIENCE ADVANCES 2022; 8:eabq4240. [PMID: 35905188 PMCID: PMC9337756 DOI: 10.1126/sciadv.abq4240] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Accepted: 06/15/2022] [Indexed: 06/15/2023]
Abstract
Metasurfaces consisting of nanoscale structures are underpinning new physical principles for the creation and shaping of quantum states of light. Multiphoton states that are entangled in spatial or angular domains are an essential resource for many quantum applications; however, their production traditionally relies on bulky nonlinear crystals. We predict and demonstrate experimentally the generation of spatially entangled photon pairs through spontaneous parametric down-conversion from a metasurface incorporating a nonlinear thin film of lithium niobate covered by a silica meta-grating. We measure the correlations of photon pairs and identify their spatial antibunching through violation of the classical Cauchy-Schwarz inequality, witnessing the presence of multimode entanglement. Simultaneously, the photon-pair rate is strongly enhanced by 450 times as compared to unpatterned films because of high-quality-factor resonances. These results pave the way to miniaturization of various quantum devices by incorporating ultrathin metasurfaces functioning as room temperature sources of quantum-entangled photons.
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Affiliation(s)
- Jihua Zhang
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - Jinyong Ma
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - Matthew Parry
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - Marcus Cai
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - Rocio Camacho-Morales
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - Lei Xu
- Advanced Optics and Photonics Laboratory, Department of Engineering, School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, UK
| | - Dragomir N. Neshev
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
| | - Andrey A. Sukhorukov
- ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University, Canberra, ACT 2601, Australia
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6
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Xu C, Xiao L, He J, Zhang H, Wei D, Hu X, Xiao M, Zhang Y. Manipulating the radial components of LG pump beam for ultrahigh-dimensional maximally entangled orbital angular momentum states. OPTICS EXPRESS 2022; 30:11120-11129. [PMID: 35473062 DOI: 10.1364/oe.452888] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 03/10/2022] [Indexed: 06/14/2023]
Abstract
High-dimensional maximally entangled orbital angular momentum (OAM) states are a promising resource for enhancing information capacity and robustness in quantum communication. However, it still lacks an effective method to increase the state dimensionality. Here, we theoretically propose an efficient scheme to generate maximally entangled OAM states of ultrahigh dimensionality by manipulating the radial components of a Laguerre-Gaussian (LG) pump beam. By optimizing the complex amplitudes of multiple radial modes of the LG pump light, one can feasibly achieve 101-dimensional OAM-based maximally entangled states. Our scheme has potential applications in high capacity quantum communication networks.
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7
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D'Errico A, Hufnagel F, Miatto F, Rezaee M, Karimi E. Full-mode characterization of correlated photon pairs generated in spontaneous downconversion. OPTICS LETTERS 2021; 46:2388-2391. [PMID: 33988590 DOI: 10.1364/ol.424619] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 04/17/2021] [Indexed: 06/12/2023]
Abstract
Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarization, position-momentum, and spatial modes. Exploring the spatial modes' correlation has hitherto been limited to the polar coordinates' azimuthal angle, and a few attempts to study Walsh mode's radial states. Here, we study the full-mode correlation, on a Laguerre-Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explore the effect of a structured pump beam possessing different spatial modes onto bi-photon spatial correlation. Finally, we use the capability to project over arbitrary spatial mode superpositions to perform the bi-photon state's full quantum tomography in a 16-dimensional subspace.
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8
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Yang HR, Wu HJ, Gao W, Rosales-Guzmán C, Zhu ZH. Parametric upconversion of Ince-Gaussian modes. OPTICS LETTERS 2020; 45:3034-3037. [PMID: 32479452 DOI: 10.1364/ol.393146] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Accepted: 04/28/2020] [Indexed: 05/28/2023]
Abstract
The Ince-Gaussian (IG) mode, a recently discovered type of structured Gaussian beam, corresponds to eigenfunctions of the paraxial wave equation in elliptical coordinates. This propagation-invariant mode is of significance in various domains, in particular, its nonlinear transformation; however, there have been few relevant studies to date. In this Letter, we report the parametric upconversion of IG modes and associated full-field selection rule for the first time, to the best of our knowledge. We demonstrate that IG signals can be perfectly upconverted by a flattop-beam pump; in contrast, significant mode distortion occurred when using the most common Gaussian pump. Particular attention was given to the origin of the distortion, i.e., radial-mode degeneration induced by the sum-frequency generation excited by a Gaussian pump. This proof-of-principle demonstration has great significance in relevant areas, such as high-dimensional quantum frequency interfacing and upconversion imaging.
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9
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Quantum mechanics with patterns of light: Progress in high dimensional and multidimensional entanglement with structured light. ACTA ACUST UNITED AC 2019. [DOI: 10.1116/1.5112027] [Citation(s) in RCA: 80] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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10
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Defienne H, Reichert M, Fleischer JW, Faccio D. Quantum image distillation. SCIENCE ADVANCES 2019; 5:eaax0307. [PMID: 31667343 PMCID: PMC6799981 DOI: 10.1126/sciadv.aax0307] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2019] [Accepted: 09/25/2019] [Indexed: 05/27/2023]
Abstract
Imaging with quantum states of light promises advantages over classical approaches in terms of resolution, signal-to-noise ratio, and sensitivity. However, quantum detectors are particularly sensitive sources of classical noise that can reduce or cancel any quantum advantage in the final result. Without operating in the single-photon counting regime, we experimentally demonstrate distillation of a quantum image from measured data composed of a superposition of both quantum and classical light. We measure the image of an object formed under quantum illumination (correlated photons) that is mixed with another image produced by classical light (uncorrelated photons) with the same spectrum and polarization, and we demonstrate near-perfect separation of the two superimposed images by intensity correlation measurements. This work provides a method to mix and distinguish information carried by quantum and classical light, which may be useful for quantum imaging, communications, and security.
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Affiliation(s)
- Hugo Defienne
- School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK
| | - Matthew Reichert
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Jason W. Fleischer
- Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Daniele Faccio
- School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK
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11
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Liu S, Liu S, Yang C, Xu Z, Li Y, Li Y, Zhou Z, Guo G, Shi B. Classical simulation of high-dimensional entanglement by non-separable angular-radial modes. OPTICS EXPRESS 2019; 27:18363-18375. [PMID: 31252781 DOI: 10.1364/oe.27.018363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Accepted: 06/04/2019] [Indexed: 06/09/2023]
Abstract
An analogous model system for high-dimensional quantum entanglement is proposed, based on the angular and radial degrees of freedom of the improved Laguerre Gaussian mode. Experimentally, we observed strong violations of the Bell-CGLMP inequality for maximally non-separable states of dimension 2 through 10. The results for violations in classical non-separable state are in very good agreement with quantum instance, which illustrates that our scheme can be a useful platform to simulate high-dimensional non-local entanglement. Additionally, we found that the Bell measurements provide sufficient criteria for identifying mode separability in a high-dimensional space. Similar to the two-dimensional spin-orbit non-separable state, the proposed high-dimensional angular-radial non-separable state may provide promising applications for classical and quantum information processing.
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12
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Wang W, Wu Z, Shang Q, Lu B. Propagation of multiple Bessel Gaussian beams through weak turbulence. OPTICS EXPRESS 2019; 27:12780-12793. [PMID: 31052814 DOI: 10.1364/oe.27.012780] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2019] [Accepted: 04/05/2019] [Indexed: 06/09/2023]
Abstract
The average intensity of the multiple Bessel Gaussian beams (mBGBs), which comprise the summation of the Bessel function and a Gaussian function, are investigated based on the extended Huygens-Fresnel principle and the Rytov theory. The weak turbulence just leads the mBGBs diverge and has no influence on the angular distribution of both the mean field and the average intensity. Therefore, the angular distribution of the average intensity depends on the average in the free space. When the order difference between any two sub beams of the mBGBs is the integer multiple of the minimum order difference, there are the symmetric side lobes of the average intensity distribution and its angular frequency is equal to the minimum order difference. Moreover, for the mBGBs with two sub beams, the initial phase change of the different sub beams could make the average intensity distribution rotate in opposite direction. This paper provides the theoretical basis for the investigation of the mBGBs propagation and the application of the sub beam detection and the beam multiplexing.
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13
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Bouchard F, Valencia NH, Brandt F, Fickler R, Huber M, Malik M. Measuring azimuthal and radial modes of photons. OPTICS EXPRESS 2018; 26:31925-31941. [PMID: 30650772 DOI: 10.1364/oe.26.031925] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 10/08/2018] [Indexed: 06/09/2023]
Abstract
With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount importance. Highly precise techniques for measuring the polarisation, frequency, and arrival time of a photon have been developed. However, the transverse spatial degree of freedom still lacks a measurement scheme that allows the reconstruction of its full transverse structure with a simple implementation and a high level of accuracy. Here we show a method to measure the azimuthal and radial modes of Laguerre-Gaussian beams with a greater than 99 % accuracy, using a single phase screen. We compare our technique with previous commonly used methods and demonstrate the significant improvements it presents for quantum key distribution and state tomography of high-dimensional quantum states of light. Moreover, our technique can be readily extended to any arbitrary family of spatial modes, such as mutually unbiased bases, Hermite-Gauss, and Ince-Gauss. Our scheme will significantly enhance existing quantum and classical communication protocols that use the spatial structure of light, as well as enable fundamental experiments on spatial-mode entanglement to reach their full potential.
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14
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Gu X, Krenn M, Erhard M, Zeilinger A. Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments. PHYSICAL REVIEW LETTERS 2018; 120:103601. [PMID: 29570339 DOI: 10.1103/physrevlett.120.103601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2017] [Indexed: 05/27/2023]
Abstract
We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete two-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment-significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multiphotonic quantum experiments.
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Affiliation(s)
- Xuemei Gu
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- State Key Laboratory for Novel Software Technology, Nanjing University, 163 Xianlin Avenue, Qixia District, 210023 Nanjing City, China
| | - Mario Krenn
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Manuel Erhard
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Anton Zeilinger
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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15
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Tasca DS, Sánchez P, Walborn SP, Rudnicki Ł. Mutual Unbiasedness in Coarse-Grained Continuous Variables. PHYSICAL REVIEW LETTERS 2018; 120:040403. [PMID: 29437426 DOI: 10.1103/physrevlett.120.040403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2017] [Revised: 11/09/2017] [Indexed: 06/08/2023]
Abstract
The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.
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Affiliation(s)
- Daniel S Tasca
- Instituto de Física, Universidade Federal Fluminense, Niterói, Rio de Janeiro 24210-346, Brazil
| | - Piero Sánchez
- Departamento de Ciencias, Sección Física, Pontificia Universidad Católica del Perú, Apartado 1761, Lima, Peru
| | - Stephen P Walborn
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
| | - Łukasz Rudnicki
- Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany
- Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
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16
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Zhou Y, Mirhosseini M, Fu D, Zhao J, Hashemi Rafsanjani SM, Willner AE, Boyd RW. Sorting Photons by Radial Quantum Number. PHYSICAL REVIEW LETTERS 2017; 119:263602. [PMID: 29328697 DOI: 10.1103/physrevlett.119.263602] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Indexed: 06/07/2023]
Abstract
The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a paraxial photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field.
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Affiliation(s)
- Yiyu Zhou
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Mohammad Mirhosseini
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Dongzhi Fu
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
- Key Laboratory for Quantum Information and Quantum Optoelectronic Devices, Department of Applied Physics, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China
| | - Jiapeng Zhao
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | | | - Alan E Willner
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Robert W Boyd
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
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17
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Zhang Y, Agnew M, Roger T, Roux FS, Konrad T, Faccio D, Leach J, Forbes A. Simultaneous entanglement swapping of multiple orbital angular momentum states of light. Nat Commun 2017; 8:632. [PMID: 28935969 PMCID: PMC5608840 DOI: 10.1038/s41467-017-00706-1] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2016] [Accepted: 07/21/2017] [Indexed: 12/03/2022] Open
Abstract
High-bit-rate long-distance quantum communication is a proposed technology for future communication networks and relies on high-dimensional quantum entanglement as a core resource. While it is known that spatial modes of light provide an avenue for high-dimensional entanglement, the ability to transport such quantum states robustly over long distances remains challenging. To overcome this, entanglement swapping may be used to generate remote quantum correlations between particles that have not interacted; this is the core ingredient of a quantum repeater, akin to repeaters in optical fibre networks. Here we demonstrate entanglement swapping of multiple orbital angular momentum states of light. Our approach does not distinguish between different anti-symmetric states, and thus entanglement swapping occurs for several thousand pairs of spatial light modes simultaneously. This work represents the first step towards a quantum network for high-dimensional entangled states and provides a test bed for fundamental tests of quantum science. Entanglement swapping in high dimensions requires large numbers of entangled photons and consequently suffers from low photon flux. Here the authors demonstrate entanglement swapping of multiple spatial modes of light simultaneously, without the need for increasing the photon numbers with dimension.
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Affiliation(s)
- Yingwen Zhang
- CSIR National Laser Centre, PO Box 395, Pretoria, 0001, South Africa.,Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada
| | - Megan Agnew
- IPaQS, SUPA, Heriot-Watt, Edinburgh, EH14 4AS, UK
| | - Thomas Roger
- IPaQS, SUPA, Heriot-Watt, Edinburgh, EH14 4AS, UK
| | - Filippus S Roux
- CSIR National Laser Centre, PO Box 395, Pretoria, 0001, South Africa.,School of Physics, University of Witwatersrand, Johannesburg, 2000, South Africa.,National Metrology Institute of South Africa, Meiring Naude Road, Pretoria, South Africa
| | - Thomas Konrad
- School of Chemistry and Physics, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa.,National Institute of Theoretical Physics, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa
| | | | | | - Andrew Forbes
- CSIR National Laser Centre, PO Box 395, Pretoria, 0001, South Africa.,School of Physics, University of Witwatersrand, Johannesburg, 2000, South Africa
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18
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Neo R, Leon-Saval S, Bland-Hawthorn J, Molina-Terriza G. OAM interferometry: the detection of the rotational Doppler shift. OPTICS EXPRESS 2017; 25:21159-21170. [PMID: 29041522 DOI: 10.1364/oe.25.021159] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2017] [Accepted: 07/11/2017] [Indexed: 06/07/2023]
Abstract
In this paper, we propose a new type of rotational Doppler shift measurement based on the OAM of light which is capable of measuring the rotation of a point source in the plane orthogonal to the observer line of sight. By analysing the correlations between OAM states of light emitted by rotating sources, the rotational Doppler shift, and hence the rate of rotation, can be measured. We demonstrate that an OAM interferometer capable of extracting the rotational Doppler shift from OAM correlations can be constructed from a standard OAM modesorter combined with a phase filter.
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19
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Krenn M, Malik M, Erhard M, Zeilinger A. Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20150442. [PMID: 28069773 PMCID: PMC5247486 DOI: 10.1098/rsta.2015.0442] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/09/2016] [Indexed: 05/17/2023]
Abstract
The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly 25 years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here, we explain the intuition that led to the first quantum experiment with OAM 15 years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps to applying these properties in novel quantum protocols. At the end, we identify several interesting open questions that could form the subject of future investigations with OAM.This article is part of the themed issue 'Optical orbital angular momentum'.
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Affiliation(s)
- Mario Krenn
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Mehul Malik
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Manuel Erhard
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Anton Zeilinger
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
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20
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Kovlakov EV, Bobrov IB, Straupe SS, Kulik SP. Spatial Bell-State Generation without Transverse Mode Subspace Postselection. PHYSICAL REVIEW LETTERS 2017; 118:030503. [PMID: 28157356 DOI: 10.1103/physrevlett.118.030503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Indexed: 06/06/2023]
Abstract
Spatial states of single photons and spatially entangled photon pairs are becoming an important resource in quantum communication. This additional degree of freedom provides an almost unlimited information capacity, making the development of high-quality sources of spatial entanglement a well-motivated research direction. We report an experimental method for generation of photon pairs in a maximally entangled spatial state. In contrast to existing techniques, the method does not require postselection of a particular subspace of spatial modes and allows one to use the full photon flux from the nonlinear crystal, providing a tool for creating high-brightness sources of pure spatially entangled photons. Such sources are a prerequisite for emerging applications in free-space quantum communication.
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Affiliation(s)
- E V Kovlakov
- Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia
| | - I B Bobrov
- Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia
| | - S S Straupe
- Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia
| | - S P Kulik
- Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia
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21
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Avetisyan H, Monken CH. Mode analysis of higher-order transverse-mode correlation beams in a turbulent atmosphere. OPTICS LETTERS 2017; 42:101-104. [PMID: 28059185 DOI: 10.1364/ol.42.000101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Due to the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric downconversion, the generated twin photons are entangled in their spatial degrees of freedom. This spatial entanglement can be observed through correlation measurements in any set of modes in which one may choose to perform measurements. Choosing, e.g., a Hermite-Gaussian (HG) set of spatial modes as a basis, one can observe correlations present in their spatial degrees of freedom. In addition, these modes can be used as alphabets for quantum communication. For global quantum communication purposes, we derive an analytic expression for two-photon detection probability in terms of HG modes, taking into account the effects of the turbulent atmosphere. Our result is more general as it accounts for the propagation of both signal and idler photons through the atmosphere, as opposed to other works considering one photon's propagation in vacuum. We show that while the restrictions on both the parity and order of the downconverted HG fields no longer hold, due to the crosstalk between modes when propagating in the atmosphere, the crosstalk is not uniform: there are more robust modes that tend to keep the photons in them. These modes can be employed in order to increase the fidelity of quantum communication.
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22
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De Assis PL, Carvalho MAD, Berruezo LP, Ferraz J, Pádua S. Generation of two pairs of qudits using four photons and a single degree of freedom. OPTICS EXPRESS 2016; 24:30149-30163. [PMID: 28059292 DOI: 10.1364/oe.24.030149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Qudits, d-level quantum systems, have been shown to provide a better resource for quantum key distribution and other Quantum Information protocols. It is customary to generate photonic qudits using more than one degree of freedom of the same photon. In much the same way, multi-qubit states are generated using only a pair of photons and ingenious ways to manipulate more than one degree of freedom independently. In contrast to such costly implementations in terms of quantum resources, we present the controlled generation of two copies of two-qudit states using four photons and a single degree of freedom, transverse momentum. The degree of entanglement within each pair was inferred by exploiting the availability of two copies of the same state, without the need of a full tomographic reconstruction of the states, and both highly-entangled and separable states were generated. We show theoretically that the set of states obtainable using our setup is very diverse, ranging from maximally entangled states of qudits to separable states.
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23
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Unternährer M, Bessire B, Gasparini L, Stoppa D, Stefanov A. Coincidence detection of spatially correlated photon pairs with a monolithic time-resolving detector array. OPTICS EXPRESS 2016; 24:28829-28841. [PMID: 27958526 DOI: 10.1364/oe.24.028829] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
We demonstrate coincidence measurements of spatially entangled photons by means of a multi-pixel based detection array. The sensor, originally developed for positron emission tomography applications, is a fully digital 8×16 silicon photomultiplier array allowing not only photon counting but also per-pixel time stamping of the arrived photons with an effective resolution of 265 ps. Together with a frame rate of 500 kfps, this property exceeds the capabilities of conventional charge-coupled device cameras which have become of growing interest for the detection of transversely correlated photon pairs. The sensor is used to measure a second-order correlation function for various non-collinear configurations of entangled photons generated by spontaneous parametric down-conversion. The experimental results are compared to theory.
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24
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Restuccia S, Giovannini D, Gibson G, Padgett M. Comparing the information capacity of Laguerre-Gaussian and Hermite-Gaussian modal sets in a finite-aperture system. OPTICS EXPRESS 2016; 24:27127-27136. [PMID: 27906287 DOI: 10.1364/oe.24.027127] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Using a spontaneous parametric down-conversion process to create entangled spatial states, we compare the information capacity associated with measurements in the Hermite-Gaussian and Laguerre-Gaussian modal basis in an optical system of finite aperture. We show that the cross-talk imposed by the aperture restriction degrades the information capacity. However, the Laguerre-Gaussian mode measurements show greater resilience to cross talk than the Hermite-Gaussian, suggesting that the Laguerre-Gaussian modal set may still offer real-world advantages over other modal sets.
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25
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Chen M, Dholakia K, Mazilu M. Is there an optimal basis to maximise optical information transfer? Sci Rep 2016; 6:22821. [PMID: 26976626 PMCID: PMC4791631 DOI: 10.1038/srep22821] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2015] [Accepted: 02/22/2016] [Indexed: 11/30/2022] Open
Abstract
We establish the concept of the density of the optical degrees of freedom that may be applied to any photonics based system. As a key example of this versatile approach we explore information transfer using optical communication. We demonstrate both experimentally, theoretically and numerically that the use of a basis set with fields containing optical vortices does not increase the telecommunication capacity of an optical system.
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Affiliation(s)
- Mingzhou Chen
- SUPA, School of Physics and Astronomy, University of St. Andrews, KY16 9SS, UK
| | - Kishan Dholakia
- SUPA, School of Physics and Astronomy, University of St. Andrews, KY16 9SS, UK
| | - Michael Mazilu
- SUPA, School of Physics and Astronomy, University of St. Andrews, KY16 9SS, UK
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26
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Hiesmayr BC, de Dood MJA, Löffler W. Observation of Four-Photon Orbital Angular Momentum Entanglement. PHYSICAL REVIEW LETTERS 2016; 116:073601. [PMID: 26943533 DOI: 10.1103/physrevlett.116.073601] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2015] [Indexed: 05/14/2023]
Abstract
We demonstrate genuine multipartite quantum entanglement of four photons in their orbital angular momentum degrees of freedom, where a high-dimensional discrete Hilbert space is attached to each photon. This can encode more quantum information compared to the qubit case, but it is a long-standing problem to entangle more than two such photons. In our experiment we use pulsed spontaneous parametric down-conversion to produce the photon quadruplets, which allows us to detect about one four-photon event per second. By means of quantum state reconstruction and a suitable witness operator we find that the photon quadruplets form a genuine multipartite entangled symmetric Dicke state. This opens a new tool for addressing foundational questions in quantum mechanics, and for exploration of novel high-dimensional multiparty quantum information applications such as secret sharing.
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Affiliation(s)
- B C Hiesmayr
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
| | - M J A de Dood
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
| | - W Löffler
- Huygens-Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands
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27
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Direct measurement of large-scale quantum states via expectation values of non-Hermitian matrices. Nat Commun 2016; 7:10439. [PMID: 26780858 PMCID: PMC4735685 DOI: 10.1038/ncomms10439] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Accepted: 12/10/2015] [Indexed: 11/26/2022] Open
Abstract
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. Non-Hermitian operators, however, are not necessarily devoid of physical significance, and they can play a crucial role in the characterization of quantum states. Here we show that the expectation values of a particular set of non-Hermitian matrices, which we call column operators, directly yield the complex coefficients of a quantum state vector. We provide a definition of the state vector in terms of measurable quantities by decomposing these column operators into observables. The technique we propose renders very-large-scale quantum states significantly more accessible in the laboratory, as we demonstrate by experimentally characterizing a 100,000-dimensional entangled state. This represents an improvement of two orders of magnitude with respect to previous phase-and-amplitude characterizations of discrete entangled states. Quantum state tomography is the process of retrieving the values that define a quantum system, but realizing it experimentally can be burdensome. Here, the authors provide an alternative approach via the expectation values of a set of non-Hermitian matrices, and characterize a 100,000-dimensional state.
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28
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Ayyoubzadeh SM, Vosoughi N. On the spatiotemporal correlations in a linear stochastic field generated by non-interacting particles: Theory. ANN NUCL ENERGY 2015. [DOI: 10.1016/j.anucene.2015.05.039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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29
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Bobrov IB, Kovlakov EV, Markov AA, Straupe SS, Kulik SP. Tomography of spatial mode detectors. OPTICS EXPRESS 2015; 23:649-654. [PMID: 25835824 DOI: 10.1364/oe.23.000649] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Transformation and detection of photons in higher-order spatial modes usually requires complicated holographic techniques. Detectors based on spatial holograms suffer from non-idealities and should be carefully calibrated. We report a novel method for analyzing the quality of projective measurements in spatial mode basis inspired by quantum detector tomography. It allows us to calibrate the detector response using only gaussian beams. We experimentally investigate the inherent inaccuracy of the existing methods of mode transformation and provide a full statistical reconstruction of the POVM (positive operator valued measure) elements for holographic spatial mode detectors.
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30
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Lu LL, Xu P, Zhong ML, Bai YF, Zhu SN. Orbital angular momentum entanglement via fork-poling nonlinear photonic crystals. OPTICS EXPRESS 2015; 23:1203-1212. [PMID: 25835879 DOI: 10.1364/oe.23.001203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report a compact scheme for the generation and manipulation of photon pairs entangled in the orbital angular momentum (OAM) from the fork-poling quadratic nonlinear crystal. The χ(2)-modulation in this crystal is designed for fulfilling a tilted quasi-phase-matching geometry to ensure the efficient generation of entangled photons as well as for transferring of topological charge of the crystal to the photon pairs. Numerical results show that the OAM of photon pair is anti-correlated and the degree of OAM entanglement can be enhanced by modulating the topological charge of crystal, which indicates a feasible extension to high-dimensional OAM entanglement. These studies suggest that the fork-poling nonlinear photonic crystal a unique platform for compact generation and manipulation of high-dimensional and high-order OAM entanglement, which may have potential applications in quantum communication, quantum cryptography and quantum remote sensing.
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31
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Practical bound for dimensionality in high-dimensional entanglement. Proc Natl Acad Sci U S A 2014; 111:6122-3. [PMID: 24737892 DOI: 10.1073/pnas.1404903111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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32
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Generation and confirmation of a (100 x 100)-dimensional entangled quantum system. Proc Natl Acad Sci U S A 2014; 111:6243-7. [PMID: 24706902 DOI: 10.1073/pnas.1402365111] [Citation(s) in RCA: 98] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing. Here we present the creation of a (100 × 100)-dimensional entangled quantum system, using spatial modes of photons. For its verification we develop a novel nonlinear criterion which infers entanglement dimensionality of a global state by using only information about its subspace correlations. This allows very practical experimental implementation as well as highly efficient extraction of entanglement dimensionality information. Applications in quantum cryptography and other protocols are very promising.
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33
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Tasca DS, Aspden RS, Morris PA, Anderson G, Boyd RW, Padgett MJ. The influence of non-imaging detector design on heralded ghost-imaging and ghost-diffraction examined using a triggered ICCD camera. OPTICS EXPRESS 2013; 21:30460-73. [PMID: 24514623 DOI: 10.1364/oe.21.030460] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Ghost imaging and ghost diffraction can be realized by using the spatial correlations between signal and idler photons produced by spontaneous parametric down-conversion. If an object is placed in the signal (idler) path, the spatial correlations between the transmitted photons as measured by a single, non-imaging, "bucket" detector and a scanning detector placed in the idler (signal) path can reveal either the image or diffraction pattern of the object, whereas neither detector signal on its own can. The details of the bucket detector, such as its collection area and numerical aperture, set the number of transverse modes supported by the system. For ghost imaging these details are less important, affecting mostly the sampling time required to produce the image. For ghost diffraction, however, the bucket detector must be filtered to a single, spatially coherent mode. We examine this difference in behavour by using either a multi-mode or single-mode fibre to define the detection aperture. Furthermore, instead of a scanning detector we use a heralded camera so that the image or diffraction pattern produced can be measured across the full field of view. The importance of a single mode detection in the observation of ghost diffraction is equivalent to the need within a classical diffraction experiment to illuminate the aperture with a spatially coherent mode.
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34
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Fickler R, Krenn M, Lapkiewicz R, Ramelow S, Zeilinger A. Real-time imaging of quantum entanglement. Sci Rep 2013; 3:1914. [PMID: 23715056 PMCID: PMC3665961 DOI: 10.1038/srep01914] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Accepted: 05/07/2013] [Indexed: 11/09/2022] Open
Abstract
Quantum Entanglement is widely regarded as one of the most prominent features of quantum mechanics and quantum information science. Although, photonic entanglement is routinely studied in many experiments nowadays, its signature has been out of the grasp for real-time imaging. Here we show that modern technology, namely triggered intensified charge coupled device (ICCD) cameras are fast and sensitive enough to image in real-time the effect of the measurement of one photon on its entangled partner. To quantitatively verify the non-classicality of the measurements we determine the detected photon number and error margin from the registered intensity image within a certain region. Additionally, the use of the ICCD camera allows us to demonstrate the high flexibility of the setup in creating any desired spatial-mode entanglement, which suggests as well that visual imaging in quantum optics not only provides a better intuitive understanding of entanglement but will improve applications of quantum science.
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Affiliation(s)
- Robert Fickler
- Quantum Optics, Quantum Nanophysics, Quantum Information, University of Vienna, Vienna, Austria.
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35
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Geelen D, Löffler W. Walsh modes and radial quantum correlations of spatially entangled photons. OPTICS LETTERS 2013; 38:4108-11. [PMID: 24321935 DOI: 10.1364/ol.38.004108] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Orthogonal sets of 2D transverse modes are key to controlling the spatial degree of freedom of light in a classical or quantum context. In contrast to the azimuthal part, which is easily accessible using orbital angular momentum modes, control of the radial part is more difficult. We show here that simple sets of orthogonal binary sequences, the Walsh functions, provide a workable solution for exploration of the radial space with phase-only spatial light modulation. We demonstrate this by measuring "sequency" quantum correlations between different radial Walsh modes of spatially entangled photon pairs and for numerically optimized versions thereof.
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36
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Giovannini D, Romero J, Leach J, Dudley A, Forbes A, Padgett MJ. Characterization of high-dimensional entangled systems via mutually unbiased measurements. PHYSICAL REVIEW LETTERS 2013; 110:143601. [PMID: 25166985 DOI: 10.1103/physrevlett.110.143601] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Indexed: 05/14/2023]
Abstract
Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multipartite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d = 2 to 5.
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Affiliation(s)
- D Giovannini
- School of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
| | - J Romero
- School of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom and Department of Physics, SUPA, University of Strathclyde, Glasgow G4 ONG, United Kingdom
| | - J Leach
- School of Engineering and Physical Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - A Dudley
- CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa
| | - A Forbes
- CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa and School of Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa
| | - M J Padgett
- School of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
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37
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McLaren M, Agnew M, Leach J, Roux FS, Padgett MJ, Boyd RW, Forbes A. Entangled Bessel-Gaussian beams. OPTICS EXPRESS 2012. [PMID: 23188323 DOI: 10.1364/oe.20.023589] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Orbital angular momentum (OAM) entanglement is investigated in the Bessel-Gaussian (BG) basis. Having a readily adjustable radial scale, BG modes provide an alternative basis for OAM entanglement over Laguerre-Gaussian modes. We show that the OAM bandwidth in terms of BG modes can be increased by selection of particular radial wavevectors and leads to a flattening of the spectrum, which allows for higher dimensionality in the entangled state. We demonstrate entanglement in terms of BG modes by performing a Bell-type experiment and showing a violation of the Clauser-Horne-Shimony-Holt inequality for the ℓ = ±1 subspace. In addition, we use quantum state tomography to indicate higher-dimensional entanglement in terms of BG modes.
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Affiliation(s)
- Melanie McLaren
- CSIR National Laser Centre, P.O. Box 395, Pretoria 0001, South Africa
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