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Lee D, Shin W, Park S, Kim J, Shin H. NOON-state interference in the frequency domain. LIGHT, SCIENCE & APPLICATIONS 2024; 13:90. [PMID: 38622155 PMCID: PMC11018870 DOI: 10.1038/s41377-024-01439-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Revised: 02/26/2024] [Accepted: 03/25/2024] [Indexed: 04/17/2024]
Abstract
The examination of entanglement across various degrees of freedom has been pivotal in augmenting our understanding of fundamental physics, extending to high dimensional quantum states, and promising the scalability of quantum technologies. In this paper, we demonstrate the photon number path entanglement in the frequency domain by implementing a frequency beam splitter that converts the single-photon frequency to another with 50% probability using Bragg scattering four-wave mixing. The two-photon NOON state in a single-mode fiber is generated in the frequency domain, manifesting the two-photon interference with two-fold enhanced resolution compared to that of single-photon interference, showing the outstanding stability of the interferometer. This successful translation of quantum states in the frequency domain will pave the way toward the discovery of fascinating quantum phenomena and scalable quantum information processing.
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Affiliation(s)
- Dongjin Lee
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, South Korea
| | - Woncheol Shin
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, South Korea
| | - Sebae Park
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, South Korea
| | - Junyeop Kim
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, South Korea
| | - Heedeuk Shin
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, South Korea.
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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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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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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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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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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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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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9
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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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10
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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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11
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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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12
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Chille V, Banzer P, Aiello A, Leuchs G, Marquardt C, Treps N, Fabre C. Quantum uncertainty in the beam width of spatial optical modes. OPTICS EXPRESS 2015; 23:32777-32787. [PMID: 26699067 DOI: 10.1364/oe.23.032777] [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
We theoretically investigate the quantum uncertainty in the beam width of transverse optical modes and, for this purpose, define a corresponding quantum operator. Single mode states are studied as well as multimode states with small quantum noise. General relations are derived, and specific examples of different modes and quantum states are examined. For the multimode case, we show that the quantum uncertainty in the beam width can be completely attributed to the amplitude quadrature uncertainty of one specific mode, which is uniquely determined by the field under investigation. This discovery provides us with a strategy for the reduction of the beam width noise by an appropriate choice of the quantum state.
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13
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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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14
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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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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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17
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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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18
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Distante E, Ježek M, Andersen UL. Deterministic superresolution with coherent states at the shot noise limit. PHYSICAL REVIEW LETTERS 2013; 111:033603. [PMID: 23909318 DOI: 10.1103/physrevlett.111.033603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2012] [Indexed: 06/02/2023]
Abstract
Interference of light fields plays an important role in various high-precision measurement schemes. It has been shown that superresolving phase measurements beyond the standard coherent state limit can be obtained either by using maximally entangled multiparticle states of light or using complex detection approaches. Here we show that superresolving phase measurements at the shot noise limit can be achieved without resorting to nonclassical optical states or to low-efficiency detection processes. Using robust coherent states of light, high-efficiency homodyne detection, and a deterministic binarization processing technique, we show a narrowing of the interference fringes that scales with 1/√[N] where N is the mean number of photons of the coherent state. Experimentally we demonstrate a 12-fold narrowing at the shot noise limit.
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Affiliation(s)
- Emanuele Distante
- Department of Physics, Technical University of Denmark, Fysikvej, 2800 Kongens Lyngby, Denmark
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19
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Shin H, Magaña-Loaiza OS, Malik M, O'Sullivan MN, Boyd RW. Enhancing entangled-state phase estimation by combining classical and quantum protocols. OPTICS EXPRESS 2013; 21:2816-2822. [PMID: 23481738 DOI: 10.1364/oe.21.002816] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Here we describe a laboratory procedure by which we have increased the resolution of a measurement of the position of an optical component by a factor of 16. The factor of 16 arises from a four-fold quantum enhancement through the use of an N = 4 N00N state and a four-fold classical enhancement from a quadruple pass through a prism pair. The possibility of achieving supersensitivity using this method is discussed.
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Affiliation(s)
- Heedeuk Shin
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA.
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