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Sperling J, Phillips DS, Bulmer JFF, Thekkadath GS, Eckstein A, Wolterink TAW, Lugani J, Nam SW, Lita A, Gerrits T, Vogel W, Agarwal GS, Silberhorn C, Walmsley IA. Detector-Agnostic Phase-Space Distributions. PHYSICAL REVIEW LETTERS 2020; 124:013605. [PMID: 31976720 DOI: 10.1103/physrevlett.124.013605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2019] [Indexed: 06/10/2023]
Abstract
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of well-known phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single- and two-photon states in phase space and certify their nonclassicality with high statistical significance.
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Affiliation(s)
- J Sperling
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - D S Phillips
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - J F F Bulmer
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - G S Thekkadath
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - A Eckstein
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - T A W Wolterink
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - J Lugani
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - S W Nam
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - A Lita
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - T Gerrits
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - W Vogel
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23, D-18059 Rostock, Germany
| | - G S Agarwal
- Texas A&M University, College Station, Texas 77845, USA
| | - C Silberhorn
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - I A Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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2
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Tiedau J, Meyer-Scott E, Nitsche T, Barkhofen S, Bartley TJ, Silberhorn C. A high dynamic range optical detector for measuring single photons and bright light. OPTICS EXPRESS 2019; 27:1-15. [PMID: 30645350 DOI: 10.1364/oe.27.000001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2018] [Accepted: 10/23/2018] [Indexed: 06/09/2023]
Abstract
Detecting light is fundamental to all optical experiments and applications. At the single photon level, the quantized nature of light requires specialised detectors, which typically saturate when more than one photon is incident. Here, we report on a massively-multiplexed single-photon detector, which exploits the saturation regime of a single click detector to exhibit a dynamic range of 123 dB, enabling measurement from optical energies as low as 10- 7 photons per pulse to ∼ 2.5 × 105photons per pulse. This allows us to calibrate a single photon detector directly to a power meter, as well as characterize the nonclassical features of a variety of quantum states.
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Bohmann M, Tiedau J, Bartley T, Sperling J, Silberhorn C, Vogel W. Incomplete Detection of Nonclassical Phase-Space Distributions. PHYSICAL REVIEW LETTERS 2018; 120:063607. [PMID: 29481264 DOI: 10.1103/physrevlett.120.063607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Indexed: 06/08/2023]
Abstract
We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.
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Affiliation(s)
- M Bohmann
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - J Tiedau
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - T Bartley
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - J Sperling
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - C Silberhorn
- Integrated Quantum Optics Group, Applied Physics, University of Paderborn, 33098 Paderborn, Germany
| | - W Vogel
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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Sperling J, Eckstein A, Clements WR, Moore M, Renema JJ, Kolthammer WS, Nam SW, Lita A, Gerrits T, Walmsley IA, Agarwal GS, Vogel W. Identification of nonclassical properties of light with multiplexing layouts. PHYSICAL REVIEW. A 2017; 96:013804. [PMID: 29670949 PMCID: PMC5901769 DOI: 10.1103/physreva.96.013804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In Sperling et al. [Phys. Rev. Lett. 118, 163602 (2017)], we introduced and applied a detector-independent method to uncover nonclassicality. Here, we extend those techniques and give more details on the performed analysis. We derive a general theory of the positive-operator-valued measure that describes multiplexing layouts with arbitrary detectors. From the resulting quantum version of a multinomial statistics, we infer nonclassicality probes based on a matrix of normally ordered moments. We discuss these criteria and apply the theory to our data which are measured with superconducting transition-edge sensors. Our experiment produces heralded multiphoton states from a parametric down-conversion light source. We show that the known notions of sub-Poisson and sub-binomial light can be deduced from our general approach, and we establish the concept of sub-multinomial light, which is shown to outperform the former two concepts of nonclassicality for our data.
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Affiliation(s)
- J. Sperling
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, England, United Kingdom
| | - A. Eckstein
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, England, United Kingdom
| | - W. R. Clements
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, England, United Kingdom
| | - M. Moore
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, England, United Kingdom
| | - J. J. Renema
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, England, United Kingdom
| | - W. S. Kolthammer
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, England, United Kingdom
| | - S. W. Nam
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - A. Lita
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - T. Gerrits
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - I. A. Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, England, United Kingdom
| | - G. S. Agarwal
- Texas A&M University, College Station, Texas 77845, USA
| | - W. Vogel
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23, D-18059 Rostock, Germany
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Sperling J, Clements WR, Eckstein A, Moore M, Renema JJ, Kolthammer WS, Nam SW, Lita A, Gerrits T, Vogel W, Agarwal GS, Walmsley IA. Detector-Independent Verification of Quantum Light. PHYSICAL REVIEW LETTERS 2017; 118:163602. [PMID: 28474918 PMCID: PMC5894853 DOI: 10.1103/physrevlett.118.163602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2017] [Indexed: 06/07/2023]
Abstract
We introduce a method for the verification of nonclassical light which is independent of the complex interaction between the generated light and the material of the detectors. This is accomplished by means of a multiplexing arrangement. Its theoretical description yields that the coincidence statistics of this measurement layout is a mixture of multinomial distributions for any classical light field and any type of detector. This allows us to formulate bounds on the statistical properties of classical states. We apply our directly accessible method to heralded multiphoton states which are detected with a single multiplexing step only and two detectors, which are in our work superconducting transition-edge sensors. The nonclassicality of the generated light is verified and characterized through the violation of the classical bounds without the need for characterizing the used detectors.
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Affiliation(s)
- J Sperling
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - W R Clements
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - A Eckstein
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - M Moore
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - J J Renema
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - W S Kolthammer
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - S W Nam
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - A Lita
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - T Gerrits
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - W Vogel
- Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23, D-18059 Rostock, Germany
| | - G S Agarwal
- Texas A&M University, College Station, Texas 77845, USA
| | - I A Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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6
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Sperling J, Bartley TJ, Donati G, Barbieri M, Jin XM, Datta A, Vogel W, Walmsley IA. Quantum Correlations from the Conditional Statistics of Incomplete Data. PHYSICAL REVIEW LETTERS 2016; 117:083601. [PMID: 27588857 DOI: 10.1103/physrevlett.117.083601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2016] [Indexed: 06/06/2023]
Abstract
We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down-conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of photodetectors.
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Affiliation(s)
- J Sperling
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - T J Bartley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - G Donati
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - M Barbieri
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy
| | - X-M Jin
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences & Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - A Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - W Vogel
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - I A Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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Smith RA, Reddy DV, Vitullo DLP, Raymer MG. Double-heralded generation of two-photon-states by spontaneous four-wave-mixing in the presence of noise. OPTICS EXPRESS 2016; 24:5809-5821. [PMID: 27136778 DOI: 10.1364/oe.24.005809] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive the equivalence between the presence of unwanted noise in the herald channel and loss in the signal channel of heralded experiments. A procedure for characterizing the noise-photon contributions, and a means of estimating the herald noise-free photon-number distribution is demonstrated.
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8
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Harnessing click detectors for the genuine characterization of light states. Sci Rep 2016; 6:19489. [PMID: 26771053 PMCID: PMC4725864 DOI: 10.1038/srep19489] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2015] [Accepted: 11/30/2015] [Indexed: 11/08/2022] Open
Abstract
The key requirement for harnessing the quantum properties of light is the capability to detect and count individual photons. Of particular interest are photon-number-resolving detectors, which allow one to determine whether a state of light is classical or genuinely quantum. Existing schemes for addressing this challenge rely on a proportional conversion of photons to electrons. As such, they are capable of correctly characterizing small photon fluxes, yet are limited by uncertainties in the conversion rate. In this work, we employ a divide-and-conquer approach to infallibly discerning non-classicality of states of light. This is achieved by transforming the incident fields into uniform spatial distributions that readily lend themselves for characterization by standard on-off detectors. Since the exact statistics of the light stream in multiplexed on-off detectors are click statistics, our technique is freely scalable to accommodate-in principle-arbitrarily large photon fluxes. Our experiments pave the way towards genuine integrated photon-number-resolving detection for advanced on-chip photonic quantum networks.
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Luis A, Sperling J, Vogel W. Nonclassicality phase-space functions: more insight with fewer detectors. PHYSICAL REVIEW LETTERS 2015; 114:103602. [PMID: 25815932 DOI: 10.1103/physrevlett.114.103602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2014] [Indexed: 06/04/2023]
Abstract
Systems of on-off detectors are well established for measuring radiation fields in the regime of small photon numbers. We propose to combine these detector systems with unbalanced homodyning with a weak local oscillator. This approach yields phase-space functions, which represent the click counterpart of the s parametrized quasiprobabilities of standard photoelectric detection theory. This introduced class of distributions can be directly sampled from the measured click-counting statistics. Therefore, our technique visualizes nonclassical effects without further data processing. Surprisingly, a small number of on-off diodes can yield more insight than perfect photon number resolution. Quantum signatures in the particle and wave domain of the quantized radiation field, as shown by photon number and squeezed states, respectively, will be uncovered in terms of negativities of the sampled phase-space functions. Application in the vast fields of quantum optics and quantum technology will benefit from our efficient nonclassicality characterization approach.
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Affiliation(s)
- Alfredo Luis
- Departamento de Óptica, Facultad de Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain
| | - Jan Sperling
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Werner Vogel
- Arbeitsgruppe Theoretische Quantenoptik, Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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Rosołek K, Stobińska M, Wieśniak M, Żukowski M. Two copies of the Einstein-Podolsky-Rosen state of light lead to refutation of EPR ideas. PHYSICAL REVIEW LETTERS 2015; 114:100402. [PMID: 25815909 DOI: 10.1103/physrevlett.114.100402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2014] [Indexed: 06/04/2023]
Abstract
Bell's theorem applies to the normalizable approximations of original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode squeezed vacuum state produced in type II down-conversion can be seen both as two copies of approximate EPR states, and also as a kind of polarization supersinglet, we show a straightforward way to test violations of the EPR concepts with direct use of their state. The observables involved are simply photon numbers at outputs of polarizing beam splitters. Suitable chained Bell inequalities are based on the geometric concept of distance. For a few settings they are potentially a new tool for quantum information applications, involving observables of a nondichotomic nature, and thus of higher informational capacity. In the limit of infinitely many settings we get a Greenberger-Horne-Zeilinger-type contradiction: EPR reasoning points to a correlation, while quantum prediction is an anticorrelation. Violations of the inequalities are fully resistant to multipair emissions in Bell experiments using parametric down-conversion sources.
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Affiliation(s)
- Krzysztof Rosołek
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
| | - Magdalena Stobińska
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Marcin Wieśniak
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
| | - Marek Żukowski
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
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Chrapkiewicz R, Wasilewski W, Banaszek K. High-fidelity spatially resolved multiphoton counting for quantum imaging applications. OPTICS LETTERS 2014; 39:5090-5093. [PMID: 25166081 DOI: 10.1364/ol.39.005090] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We present a method for spatially resolved multiphoton counting based on an intensified camera with the retrieval of multimode photon statistics fully accounting for nonlinearities in the detection process. The scheme relies on one-time quantum tomographic calibration of the detector. Faithful, high-fidelity reconstruction of single- and two-mode statistics of multiphoton states is demonstrated for coherent states and their statistical mixtures. The results consistently exhibit classical values of the Mandel parameter and the noise reduction factor in contrast to raw statistics of camera photo-events. Detector operation is reliable for illumination levels up to the average of one detected photon per an event area-substantially higher than in previous approaches to characterize quantum statistical properties of light with spatial resolution.
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