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Kudyshev ZA, Sychev D, Martin Z, Yesilyurt O, Bogdanov SI, Xu X, Chen PG, Kildishev AV, Boltasseva A, Shalaev VM. Machine learning assisted quantum super-resolution microscopy. Nat Commun 2023; 14:4828. [PMID: 37563106 PMCID: PMC10415374 DOI: 10.1038/s41467-023-40506-4] [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: 07/08/2021] [Accepted: 07/26/2023] [Indexed: 08/12/2023] Open
Abstract
One of the main characteristics of optical imaging systems is spatial resolution, which is restricted by the diffraction limit to approximately half the wavelength of the incident light. Along with the recently developed classical super-resolution techniques, which aim at breaking the diffraction limit in classical systems, there is a class of quantum super-resolution techniques which leverage the non-classical nature of the optical signals radiated by quantum emitters, the so-called antibunching super-resolution microscopy. This approach can ensure a factor of [Formula: see text] improvement in the spatial resolution by measuring the n -th order autocorrelation function. The main bottleneck of the antibunching super-resolution microscopy is the time-consuming acquisition of multi-photon event histograms. We present a machine learning-assisted approach for the realization of rapid antibunching super-resolution imaging and demonstrate 12 times speed-up compared to conventional, fitting-based autocorrelation measurements. The developed framework paves the way to the practical realization of scalable quantum super-resolution imaging devices that can be compatible with various types of quantum emitters.
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Affiliation(s)
- Zhaxylyk A Kudyshev
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA
| | - Demid Sychev
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA
| | - Zachariah Martin
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA
| | - Omer Yesilyurt
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA
| | - Simeon I Bogdanov
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
- Nick Holonyak, Jr. Micro and Nanotechnology Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Xiaohui Xu
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA
| | - Pei-Gang Chen
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA
| | - Alexander V Kildishev
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
| | - Alexandra Boltasseva
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA.
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA.
| | - Vladimir M Shalaev
- School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, USA
- The Quantum Science Center (QSC), a National Quantum Information Science Research Center of the U.S. Department of Energy (DOE), Oak Ridge, TN, USA
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2
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Howell JC, Jordan AN, Šoda B, Kempf A. Super Interferometric Range Resolution. PHYSICAL REVIEW LETTERS 2023; 131:053803. [PMID: 37595228 DOI: 10.1103/physrevlett.131.053803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 06/13/2023] [Indexed: 08/20/2023]
Abstract
We probe the fundamental underpinnings of range resolution in coherent remote sensing. We use a novel class of self-referential interference functions to show that we can greatly improve upon currently accepted bounds for range resolution. We consider the range resolution problem from the perspective of single-parameter estimation of amplitude versus the traditional temporally resolved paradigm. We define two figures of merit: (i) the minimum resolvable distance between two depths and (ii) for temporally subresolved peaks, the depth resolution between the objects. We experimentally demonstrate that our system can resolve two depths greater than 100× the inverse bandwidth and measure the distance between two objects to approximately 20 μm (35 000 times smaller than the Rayleigh-resolved limit) for temporally subresolved objects using frequencies less than 120 MHz radio waves.
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Affiliation(s)
- John C Howell
- Institute for Quantum Studies, Chapman University, Orange, California 92866, USA
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel, 91904
| | - Andrew N Jordan
- Institute for Quantum Studies, Chapman University, Orange, California 92866, USA
- Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Barbara Šoda
- Department of Applied Mathematics and Department of Physics, University of Waterloo, and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
| | - Achim Kempf
- Department of Applied Mathematics and Department of Physics, University of Waterloo, and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
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3
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Dou LY, Cao DZ, Gao L, Song XB. Sub-Rayleigh dark-field imaging via speckle illumination. OPTICS LETTERS 2023; 48:1347-1350. [PMID: 36946924 DOI: 10.1364/ol.483612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
We demonstrate sub-Rayleigh dark-field imaging via speckle illumination. Imaging is achieved with second-order autocorrelated measurement by illuminating objects with hollow conical pseudothermal light. Our scheme can work well for highly transparent amplitude objects, pure phase objects, and even more complex transparent objects. The autocorrelated dark-field images show better resolution than intensity-averaged images and an ability in filtering out low-frequency noises.
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4
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Hayama K, Cao B, Okamoto R, Suezawa S, Okano M, Takeuchi S. High-depth-resolution imaging of dispersive samples using quantum optical coherence tomography. OPTICS LETTERS 2022; 47:4949-4952. [PMID: 36181158 DOI: 10.1364/ol.469874] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 08/27/2022] [Indexed: 06/16/2023]
Abstract
Quantum optical coherence tomography (QOCT) is a promising approach to overcome the degradation of the resolution in optical coherence tomography (OCT) due to dispersion. Here, we report on an experimental demonstration of QOCT imaging in the high-resolution regime. We achieved a depth resolution of 2.5 μm, which is the highest value for QOCT imaging, to the best of our knowledge. We show that the QOCT image of a dispersive material remains clear whereas the OCT image is drastically degraded.
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5
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Camphausen R, Cuevas Á, Duempelmann L, Terborg RA, Wajs E, Tisa S, Ruggeri A, Cusini I, Steinlechner F, Pruneri V. A quantum-enhanced wide-field phase imager. SCIENCE ADVANCES 2021; 7:eabj2155. [PMID: 34788099 PMCID: PMC8598016 DOI: 10.1126/sciadv.abj2155] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Quantum techniques can be used to enhance the signal-to-noise ratio in optical imaging. Leveraging the latest advances in single-photon avalanche diode array cameras and multiphoton detection techniques, here, we introduce a supersensitive phase imager, which uses space-polarization hyperentanglement to operate over a large field of view without the need of scanning operation. We show quantum-enhanced imaging of birefringent and nonbirefringent phase samples over large areas, with sensitivity improvements over equivalent classical measurements carried out with equal number of photons. The potential applicability is demonstrated by imaging a biomedical protein microarray sample. Our technology is inherently scalable to high-resolution images and represents an essential step toward practical quantum-enhanced imaging.
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Affiliation(s)
- Robin Camphausen
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain
- Corresponding author. (R.C.); (Á.C.); (V.P.)
| | - Álvaro Cuevas
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain
- Corresponding author. (R.C.); (Á.C.); (V.P.)
| | - Luc Duempelmann
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain
| | - Roland A. Terborg
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain
| | - Ewelina Wajs
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain
| | - Simone Tisa
- Micro Photon Device SRL, Via Waltraud Gebert Deeg 3f, 39100 Bolzano, Italy
| | - Alessandro Ruggeri
- Micro Photon Device SRL, Via Waltraud Gebert Deeg 3f, 39100 Bolzano, Italy
| | - Iris Cusini
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Via Giuseppe Ponzio, 34, 20133 Milano, Italy
| | - Fabian Steinlechner
- Fraunhofer Institute for Applied Optics and Precision Engineering IOF, Albert-Einstein-Str. 7, 07745 Jena, Germany
- Abbe Center of Photonics, Friedrich Schiller University Jena, Albert-Einstein-Str. 6, 07745 Jena, Germany
| | - Valerio Pruneri
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss, 3, 08860 Castelldefels, Barcelona, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain
- Corresponding author. (R.C.); (Á.C.); (V.P.)
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6
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Chae BG. Wide viewing-angle holographic display based on enhanced-NA Fresnel hologram. OPTICS EXPRESS 2021; 29:38221-38236. [PMID: 34808879 DOI: 10.1364/oe.435424] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 09/17/2021] [Indexed: 06/13/2023]
Abstract
The viewing-angle enlargement of a holographic image is a crucial factor for realizing the holographic display. The numerical aperture (NA) of digital hologram other than a pixel specification has been known to determine the angular field extent of image. Here, we provide a valid foundation for the dependence of viewing angle on the hologram numerical aperture by investigating mathematically the internal structure of the sampled point spread function showing a self-similarity of its modulating curve. The enhanced-NA Fresnel hologram reconstructs the image at a viewing angle larger than a diffraction angle by a hologram pixel pitch where its angle value is expressed in terms of the NA of whole hologram aperture, which is observed systematically by optical experiments. Finally, we found that the aliased replica noises generated in the enhanced-NA Fresnel diffraction regime are effectively suppressed within the diffraction scope by a digitized pixel. This characteristic enables us to overcome the image reduction and to remove the interference of high-order images, which leads to the wide viewing-angle holographic display.
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7
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Bearne KKM, Zhou Y, Braverman B, Yang J, Wadood SA, Jordan AN, Vamivakas AN, Shi Z, Boyd RW. Confocal super-resolution microscopy based on a spatial mode sorter. OPTICS EXPRESS 2021; 29:11784-11792. [PMID: 33984953 DOI: 10.1364/oe.419493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 03/24/2021] [Indexed: 06/12/2023]
Abstract
Spatial resolution is one of the most important specifications of an imaging system. Recent results in the quantum parameter estimation theory reveal that an arbitrarily small distance between two incoherent point sources can always be efficiently determined through the use of a spatial mode sorter. However, extending this procedure to a general object consisting of many incoherent point sources remains challenging, due to the intrinsic complexity of multi-parameter estimation problems. Here, we generalize the Richardson-Lucy (RL) deconvolution algorithm to address this challenge. We simulate its application to an incoherent confocal microscope, with a Zernike spatial mode sorter replacing the pinhole used in a conventional confocal microscope. We test different spatially incoherent objects of arbitrary geometry, and we find that the resolution enhancement of sorter-based microscopy is on average over 30% higher than that of a conventional confocal microscope using the standard RL deconvolution algorithm. Our method could potentially be used in diverse applications such as fluorescence microscopy and astronomical imaging.
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8
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Anwar A, Perumangatt C, Steinlechner F, Jennewein T, Ling A. Entangled photon-pair sources based on three-wave mixing in bulk crystals. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2021; 92:041101. [PMID: 34243479 DOI: 10.1063/5.0023103] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2020] [Accepted: 03/01/2021] [Indexed: 06/13/2023]
Abstract
Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.
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Affiliation(s)
- Ali Anwar
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, S117543 Singapore, Singapore
| | - Chithrabhanu Perumangatt
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, S117543 Singapore, Singapore
| | - Fabian Steinlechner
- Fraunhofer Institute for Applied Optics and Precision Engineering IOF, Albert-Einstein-Straße 7, 07745 Jena, Germany
| | - Thomas Jennewein
- Institute of Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Ave. W, Waterloo, Ontario N2L 3G1, Canada
| | - Alexander Ling
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, S117543 Singapore, Singapore
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9
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10
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Kura N, Ueda M. Standard Quantum Limit and Heisenberg Limit in Function Estimation. PHYSICAL REVIEW LETTERS 2020; 124:010507. [PMID: 31976685 DOI: 10.1103/physrevlett.124.010507] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Indexed: 06/10/2023]
Abstract
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology for a spatially varying phase operator, where various degrees of smooth functions are considered. The error bounds are identified in the cases of the absence and the presence of interparticle entanglement, which correspond to the standard quantum limit and the Heisenberg limit, respectively. Notably, these error bounds can be reached by either position-localized states or wave-number-localized ones. In fact, we show that these error bounds are theoretically optimal for any type of probe states, indicating that quantum metrology on functions is also subject to the Nyquist-Shannon sampling theorem, even if classical detection is replaced by quantum measurement.
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Affiliation(s)
- Naoto Kura
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
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11
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A Review of Super-Resolution Imaging through Optical High-Order Interference [Invited]. APPLIED SCIENCES-BASEL 2019. [DOI: 10.3390/app9061166] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Resolution is crucially important for optical imaging, which defines the smallest spatial feature of object that can be delivered by light wave. However, due to the wave nature of light, optical imaging is of limited resolution, widely known as Rayleigh limit or Abbe limit. Nevertheless, this limit can be overcome by considering the loopholes in the derivation of the Rayleigh limit, such as light–matter interaction, structured illumination, and near-field interference. In contrast to the conventional single-photon interference, multi-photon amplitudes responsible for optical high-order interference could be designed to possess a reduced effective wavelength, enabling the breakthrough of the Rayleigh limit. In this review, we will present recently developed super-resolution imaging schemes based on optical high-order interference, and discuss future perspectives.
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12
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Parniak M, Borówka S, Boroszko K, Wasilewski W, Banaszek K, Demkowicz-Dobrzański R. Beating the Rayleigh Limit Using Two-Photon Interference. PHYSICAL REVIEW LETTERS 2018; 121:250503. [PMID: 30608849 DOI: 10.1103/physrevlett.121.250503] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2018] [Revised: 10/03/2018] [Indexed: 06/09/2023]
Abstract
Multiparameter estimation theory offers a general framework to explore imaging techniques beyond the Rayleigh limit. While optimal measurements of single parameters characterizing a composite light source are now well understood, simultaneous determination of multiple parameters poses a much greater challenge that in general requires implementation of collective measurements. Here we show, theoretically and experimentally, that Hong-Ou-Mandel interference followed by spatially resolved detection of photons provides precise information on both the separation and the centroid for a pair of point emitters, avoiding trade-offs inherent to single-photon measurements.
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Affiliation(s)
- Michał Parniak
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Sebastian Borówka
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Kajetan Boroszko
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Wojciech Wasilewski
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
| | - Konrad Banaszek
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
- Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
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13
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Li L, Hong P, Zhang G. Experimental realization of Heisenberg-limit resolution imaging through a phase-controlled screen with classical light. OPTICS EXPRESS 2018; 26:18950-18956. [PMID: 30114154 DOI: 10.1364/oe.26.018950] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Accepted: 07/02/2018] [Indexed: 06/08/2023]
Abstract
By using a dynamically phase-controlled screen proposed in [Opt. Express 25, 22789 (2017)], we demonstrated experimentally a correlation imaging scheme with its spatial resolution reaching the fundamental Heisenberg limit. In the experiments, the dynamically phase-controlled screen was realized through a commercial spatial light modulator by dynamically loading computer generated phase patterns, and the scanning-focused-beam illumination mode was employed to achieve the Heisenberg-resolution imaging with classical light such as laser and pseudo-thermal light.
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14
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Tham WK, Ferretti H, Steinberg AM. Beating Rayleigh's Curse by Imaging Using Phase Information. PHYSICAL REVIEW LETTERS 2017; 118:070801. [PMID: 28256878 DOI: 10.1103/physrevlett.118.070801] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Indexed: 06/06/2023]
Abstract
Every imaging system has a resolution limit, typically defined by Rayleigh's criterion. Given a fixed number of photons, the amount of information one can gain from an image about the separation between two sources falls to zero as the separation drops below this limit, an effect dubbed "Rayleigh's curse." Recently, in a quantum-information-inspired proposal, Tsang and co-workers found that there is, in principle, infinitely more information present in the full electromagnetic field in the image plane than in the intensity alone, and suggested methods for extracting this information and beating the Rayleigh limit. In this Letter, we experimentally demonstrate a simple scheme that captures most of this information, and show that it has a greatly improved ability to estimate the distance between a pair of closely separated sources, achieving near-quantum-limited performance and immunity to Rayleigh's curse.
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Affiliation(s)
- Weng-Kian Tham
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, Canada, M5S 1A7
| | - Hugo Ferretti
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, Canada, M5S 1A7
| | - Aephraim M Steinberg
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, Canada, M5S 1A7
- Canadian Institute For Advanced Research, 180 Dundas St. W., Toronto, Ontario, Canada, M5G 1Z8
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15
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Tham WK, Ferretti H, Sadashivan AV, Steinberg AM. Simulating and Optimising Quantum Thermometry Using Single Photons. Sci Rep 2016; 6:38822. [PMID: 27974836 PMCID: PMC5156908 DOI: 10.1038/srep38822] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Accepted: 11/14/2016] [Indexed: 11/09/2022] Open
Abstract
A classical thermometer typically works by exchanging energy with the system being measured until it comes to equilibrium, at which point the readout is related to the final energy state of the thermometer. A recent paper noted that with a quantum thermometer consisting of a single spin/qubit, temperature discrimination is better achieved at finite times rather than once equilibration is essentially complete. Furthermore, preparing a qubit thermometer in a state with quantum coherence instead of an incoherent one improves its sensitivity to temperature differences. Implementing a recent proposal for efficiently emulating an arbitrary quantum channel, we use the quantum polarisation state of individual photons as models of "single-qubit thermometers" which evolve for a certain time in contact with a thermal bath. We investigate the optimal thermometer states for temperature discrimination, and the optimal interaction times, confirming that there is a broad regime where quantum coherence provides a significant improvement. We also discuss the more practical question of thermometers composed of a finite number of spins/qubits (greater than one), and characterize the performance of an adaptive protocol for making optimal use of all the qubits.
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Affiliation(s)
- W K Tham
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada
| | - H Ferretti
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada
| | - A V Sadashivan
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada
| | - A M Steinberg
- Centre for Quantum Information &Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St. George St, Toronto, Ontario, M5S 1A7, Canada.,Canadian Institute For Advanced Research, 180 Dundas St. W., Toronto, Ontario, M5G 1Z8, Canada
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16
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Lupo C, Pirandola S. Ultimate Precision Bound of Quantum and Subwavelength Imaging. PHYSICAL REVIEW LETTERS 2016; 117:190802. [PMID: 27858426 DOI: 10.1103/physrevlett.117.190802] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2016] [Indexed: 06/06/2023]
Abstract
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First, we show that the problem of estimating the separation between two pointlike sources is equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Using this representation, we establish the ultimate precision bound for resolving two pointlike sources in an arbitrary quantum state, with a simple formula for the specific case of two thermal sources. We find that the precision bound scales with the number of collected photons according to the standard quantum limit. Then, we determine the sources whose separation can be estimated optimally, finding that quantum-correlated sources (entangled or discordant) can be superresolved at the sub-Rayleigh scale. Our results apply to a variety of imaging setups, from astronomical observation to microscopy, exploiting quantum detection as well as source engineering.
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Affiliation(s)
- Cosmo Lupo
- York Centre for Quantum Technologies (YCQT), University of York, York YO10 5GH, United Kingdom
| | - Stefano Pirandola
- York Centre for Quantum Technologies (YCQT), University of York, York YO10 5GH, United Kingdom
- Computer Science, University of York, York YO10 5GH, United Kingdom
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17
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Jachura M, Chrapkiewicz R, Demkowicz-Dobrzański R, Wasilewski W, Banaszek K. Mode engineering for realistic quantum-enhanced interferometry. Nat Commun 2016; 7:11411. [PMID: 27125782 PMCID: PMC4855535 DOI: 10.1038/ncomms11411] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2015] [Accepted: 03/22/2016] [Indexed: 11/21/2022] Open
Abstract
Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques. Practical quantum-enhanced interferometry is, however, vulnerable to imperfections such as partial distinguishability of interfering photons. Here we introduce a method where appropriate design of the modal structure of input photons can alleviate deleterious effects caused by another, experimentally inaccessible degree of freedom. This result is accompanied by a laboratory demonstration that a suitable choice of spatial modes combined with position-resolved coincidence detection restores entanglement-enhanced precision in the full operating range of a realistic two-photon Mach–Zehnder interferometer, specifically around a point which otherwise does not even attain the shot-noise limit due to the presence of residual distinguishing information in the spectral degree of freedom. Our method highlights the potential of engineering multimode physical systems in metrologic applications. Quantum interferometry suffers from residual distinguishability between input photons. Here, the authors show theoretically and experimentally, in a two-photon measurement, how to overcome this by manipulating additional degrees of freedom.
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Affiliation(s)
- Michał Jachura
- Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw, 02-093, Poland
| | | | | | - Wojciech Wasilewski
- Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw, 02-093, Poland
| | - Konrad Banaszek
- Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw, 02-093, Poland
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18
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Zhang E, Lin H, Liu W, Li Q, Chen P. Sub-Rayleigh-diffraction imaging via modulating classical light. OPTICS EXPRESS 2015; 23:33506-33513. [PMID: 26832015 DOI: 10.1364/oe.23.033506] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The spatial resolution of a traditional imaging system is restricted by the Rayleigh diffraction limit. In this paper, two types of classical light sources are generated by modulating the amplitude distribution and wavefront of a laser beam randomly, and the generated light sources can exhibit the features of the superposition of two-photon Fock states and the incoherent mixture of two-photon Fock states, respectively. With the generated light sources, the two-fold coherent and incoherent imaging schemes can be achieved, which lead to spatial resolution enhancement, and exceed the Rayleigh diffraction limit in the imaging system.
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19
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Guevara I, Wiseman H. Quantum State Smoothing. PHYSICAL REVIEW LETTERS 2015; 115:180407. [PMID: 26565446 DOI: 10.1103/physrevlett.115.180407] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2015] [Indexed: 06/05/2023]
Abstract
Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both earlier and later) observations. Here we define a smoothed quantum state for a partially monitored open quantum system, conditioned on an all-time monitoring-derived record. We calculate the smoothed distribution for a hypothetical unobserved record which, when added to the real record, would complete the monitoring, yielding a pure-state "quantum trajectory." Averaging the pure state over this smoothed distribution yields the (mixed) smoothed quantum state. We study how the choice of actual unraveling affects the purity increase over that of the conventional (filtered) state conditioned only on the past record.
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Affiliation(s)
- Ivonne Guevara
- Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Howard Wiseman
- Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
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20
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Zhang EF, Liu WT, Chen PX. High-resolution interference with programmable classical incoherent light. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2015; 32:1251-1255. [PMID: 26367153 DOI: 10.1364/josaa.32.001251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
A scheme of high-resolution interference with classical incoherent light is proposed. In this scheme, the classical incoherent light is programmable in the amplitude distribution and wavefront, and with the programmable classical incoherent light we improve the resolution of the interference pattern by a factor of 2 compared with the scheme by Erkmen [J. Opt. Soc. Am. A29, 782 (2012)JOAOD60740-323210.1364/JOSAA.29.000782]. Compared with other schemes for observing interference patterns, only single-pixel detection is needed in our proposal. Moreover, the high-resolution interference pattern can be inverted to obtain an image with better resolution compared with that of the scheme proposed by Erkmen. Furthermore, this scheme of high-resolution interference is verified in detail by theoretical analysis and numerical simulations.
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21
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Rozema LA, Bateman JD, Mahler DH, Okamoto R, Feizpour A, Hayat A, Steinberg AM. Scalable spatial superresolution using entangled photons. PHYSICAL REVIEW LETTERS 2014; 112:223602. [PMID: 24949765 DOI: 10.1103/physrevlett.112.223602] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2013] [Indexed: 06/03/2023]
Abstract
N00N states-maximally path-entangled states of N photons-exhibit spatial interference patterns sharper than any classical interference pattern. This is known as superresolution. However, even given perfectly efficient number-resolving detectors, the detection efficiency of all previous measurements of such interference would decrease exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. A technique known as the "optical centroid measurement" has been proposed to solve this and has been experimentally verified for photon pairs; here we present the first extension beyond two photons, measuring the superresolution fringes of two-, three-, and four-photon N00N states. Moreover, we compare the N00N-state interference to the corresponding classical superresolution interference. Although both provide the same increase in spatial frequency, the visibility of the classical fringes decreases exponentially with the number of detected photons. Our work represents an essential step forward for quantum-enhanced measurements, overcoming what was believed to be a fundamental challenge to quantum metrology.
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Affiliation(s)
- Lee A Rozema
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - James D Bateman
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Dylan H Mahler
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Ryo Okamoto
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada and Research Institute for Electronic Science, Hokkaido University, Kita-ku, Sapporo 060-0812, Japan and The Institute of Scientific and Industrial Research, Osaka University, Mihogaoka 8-1, Ibaraki, Osaka 567-0047, Japan
| | - Amir Feizpour
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Alex Hayat
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada and Department of Electrical Engineering, Technion, Haifa 32000, Israel and Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - Aephraim M Steinberg
- Centre for Quantum Information & Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada and Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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22
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23
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Super sub-wavelength patterns in photon coincidence detection. Sci Rep 2014; 4:4068. [PMID: 24531057 PMCID: PMC3925945 DOI: 10.1038/srep04068] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2013] [Accepted: 01/21/2014] [Indexed: 11/30/2022] Open
Abstract
High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.
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24
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Schwartz O, Levitt JM, Tenne R, Itzhakov S, Deutsch Z, Oron D. Superresolution microscopy with quantum emitters. NANO LETTERS 2013; 13:5832-6. [PMID: 24195698 DOI: 10.1021/nl402552m] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
The optical diffraction limit imposes a bound on imaging resolution in classical optics. Over the last twenty years, many theoretical schemes have been presented for overcoming the diffraction barrier in optical imaging using quantum properties of light. Here, we demonstrate a quantum superresolution imaging method taking advantage of nonclassical light naturally produced in fluorescence microscopy due to photon antibunching, a fundamentally quantum phenomenon inhibiting simultaneous emission of multiple photons. Using a photon counting digital camera, we detect antibunching-induced second and third order intensity correlations and perform subdiffraction limited quantum imaging in a standard wide-field fluorescence microscope.
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Affiliation(s)
- Osip Schwartz
- Department of Physics of Complex Systems, Weizmann Institute of Science , Rehovot, Israel , 76100
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25
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Humphreys PC, Barbieri M, Datta A, Walmsley IA. Quantum enhanced multiple phase estimation. PHYSICAL REVIEW LETTERS 2013; 111:070403. [PMID: 23992052 DOI: 10.1103/physrevlett.111.070403] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2013] [Indexed: 06/02/2023]
Abstract
We study the simultaneous estimation of multiple phases as a discretized model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each individual phase separately as well as improvements over classical strategies. Our strategy provides an advantage in the variance of the estimation over individual quantum estimation schemes that scales as O(d), where d is the number of phases. Finally, we study the attainability of this limit using realistic probes and photon-number-resolving detectors. This is a problem in which an intrinsic advantage is derived from the estimation of multiple parameters simultaneously.
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Affiliation(s)
- Peter C Humphreys
- Department of Physics, Clarendon Laboratory, University of Oxford, Oxford, United Kingdom.
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26
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Oh JE, Cho YW, Scarcelli G, Kim YH. Sub-Rayleigh imaging via speckle illumination. OPTICS LETTERS 2013; 38:682-4. [PMID: 23455264 PMCID: PMC4617630 DOI: 10.1364/ol.38.000682] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
We demonstrate sub-Rayleigh limit imaging of an object via speckle illumination. Imaging beyond the conventional Rayleigh limit is achieved by illuminating the object with pseudothermal light that exhibits a random speckle pattern. An object image is reconstructed from the second-order correlation measurement and the resolution of the image, which exceeds the Rayleigh limit, is shown to be related to the size of the speckle pattern that is tied to the lateral coherence length of the pseudothermal light.
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Affiliation(s)
- Joo-Eon Oh
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, South Korea
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27
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Practical photon number detection with electric field-modulated silicon avalanche photodiodes. Nat Commun 2012; 3:644. [DOI: 10.1038/ncomms1641] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2011] [Accepted: 12/14/2011] [Indexed: 11/08/2022] Open
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28
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Nair R, Yen BJ. Optimal quantum states for image sensing in loss. PHYSICAL REVIEW LETTERS 2011; 107:193602. [PMID: 22181605 DOI: 10.1103/physrevlett.107.193602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2011] [Indexed: 05/25/2023]
Abstract
We consider a general image sensing framework that includes many quantum sensing problems by an appropriate choice of image set, prior probabilities, and cost function. For any such problem, in the presence of loss and a signal energy constraint, we show that a pure input state of light with the signal modes in a mixture of number states minimizes the cost among all ancilla-assisted parallel strategies. Lossy binary phase discrimination with a peak photon number constraint and general lossless image sensing are considered as examples.
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Affiliation(s)
- Ranjith Nair
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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29
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Shin H, Chan KWC, Chang HJ, Boyd RW. Quantum spatial superresolution by optical centroid measurements. PHYSICAL REVIEW LETTERS 2011; 107:083603. [PMID: 21929168 DOI: 10.1103/physrevlett.107.083603] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2011] [Revised: 07/18/2011] [Indexed: 05/31/2023]
Abstract
Quantum lithography (QL) has been suggested as a means of achieving enhanced spatial resolution for optical imaging, but its realization has been held back by the low multiphoton detection rates of recording materials. Recently, an optical centroid measurement (OCM) procedure was proposed as a way to obtain spatial resolution enhancement identical to that of QL but with higher detection efficiency (M. Tsang, Phys. Rev. Lett. 102, 253601 (2009)). Here we describe a variation of the OCM method with still higher detection efficiency based on the use of photon-number-resolving detection. We also report laboratory results for two-photon interference. We compare these results with those of the standard QL method based on multiphoton detection and show that the new method leads to superresolution but with higher detection efficiency.
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Affiliation(s)
- Heedeuk Shin
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
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30
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Mouradian S, Wong FNC, Shapiro JH. Achieving sub-Rayleigh resolution via thresholding. OPTICS EXPRESS 2011; 19:5480-5488. [PMID: 21445186 DOI: 10.1364/oe.19.005480] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Diffraction from a finite-diameter entrance pupil imposes the Rayleigh bound on the spatial resolution achievable by a conventional imaging system. We demonstrate resolution beyond this limit through unstructured scanning of a focused laser beam across an object together with dynamic application of a threshold N less than the maximum count level Nmax. Experimental results show sub-Rayleigh resolution enhancement by a factor of [ln(Nmax/N)]1/2.
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Affiliation(s)
- Sara Mouradian
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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31
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Guerrieri F, Maccone L, Wong FNC, Shapiro JH, Tisa S, Zappa F. Sub-Rayleigh imaging via N-photon detection. PHYSICAL REVIEW LETTERS 2010; 105:163602. [PMID: 21230971 DOI: 10.1103/physrevlett.105.163602] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2010] [Indexed: 05/30/2023]
Abstract
The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ∼(N-N(max))(½) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.
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Affiliation(s)
- Fabrizio Guerrieri
- Dipartimento di Elettronica e Informazione, Politecnico di Milano, 20133 Milano, Italy
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