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Cuzminschi M, Zubarev A, Iordache SM, Isar A. Influence of the seed of measurement on the work extracted in a quantum Szilard engine. iScience 2023; 26:108563. [PMID: 38162018 PMCID: PMC10755042 DOI: 10.1016/j.isci.2023.108563] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Revised: 09/20/2023] [Accepted: 11/20/2023] [Indexed: 01/03/2024] Open
Abstract
We investigate the influence of the seed of measurement on the performance of a Szilard engine based on a two-mode Gaussian state evolving in a noisy channel. Quantum work is extracted by performing a positive operator-valued measurement (POVM) on one of the two modes, after which this mode reaches equilibrium with the environment. As the seed of measurement, we use a single-mode squeezed thermal state. We employ the Markovian Kossakowski-Lindblad master equation to determine the evolution in time of the considered open system and the quantum work is defined based on the Rényi entropy of order 2. We show that the extracted quantum work and information-work efficiency strongly depend on the characteristic parameters of the system (frequency, average thermal photons number, and squeezing), the noisy channel (temperature and squeezing of the bath), and the seed of measurement (average thermal photons number and strength of the measurement).
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Affiliation(s)
- Marina Cuzminschi
- Department of Theoretical Physics, “Horia Hulubei” National Institute for Physics and Nuclear Engineering, 07125 Magurele, Ilfov, Romania
- Faculty of Physics, University of Bucharest, 077125 Magurele, Ilfov, Romania
| | - Alexei Zubarev
- Plasma Physics and Nuclear Fusion Laboratory, National Institute for Laser, Plasma and Radiation Physics, 077125 Magurele, Ilfov, Romania
- Extreme Light Infrastructure, National Institute for Physics and Nuclear Engineering, 07125 Magurele, Ilfov, Romania
| | - Stefan-Marian Iordache
- Optospintronics Department, National Institute for Research and Development for Optoelectronics—INOE 2000, 077125 Magurele, Ilfov, Romania
| | - Aurelian Isar
- Department of Theoretical Physics, “Horia Hulubei” National Institute for Physics and Nuclear Engineering, 07125 Magurele, Ilfov, Romania
- Faculty of Physics, University of Bucharest, 077125 Magurele, Ilfov, Romania
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2
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Singh V, Müstecaplıoğlu ÖE. Performance bounds of nonadiabatic quantum harmonic Otto engine and refrigerator under a squeezed thermal reservoir. Phys Rev E 2021; 102:062123. [PMID: 33466082 DOI: 10.1103/physreve.102.062123] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 11/16/2020] [Indexed: 11/07/2022]
Abstract
We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.
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Affiliation(s)
- Varinder Singh
- Department of Physics, Koç University, 34450 Sarıyer, Istanbul, Turkey
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Qi H, Brod DJ, Quesada N, García-Patrón R. Regimes of Classical Simulability for Noisy Gaussian Boson Sampling. PHYSICAL REVIEW LETTERS 2020; 124:100502. [PMID: 32216428 DOI: 10.1103/physrevlett.124.100502] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Revised: 12/05/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
As a promising candidate for exhibiting quantum computational supremacy, Gaussian boson sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS-in the form of an inequality between the input squeezing parameter, the overall transmission rate, and the quality of photon detectors. Our result serves as a nonclassicality test that must be passed by any quantum computational supremacy demonstration based on GBS. We show that, for most linear-optical architectures, where photon loss increases exponentially with the circuit depth, noisy GBS loses its quantum advantage in the asymptotic limit. Our results thus delineate intermediate-sized regimes where GBS devices might considerably outperform classical computers for modest noise levels. Finally, we find that increasing the amount of input squeezing is helpful to evade our classical simulation algorithm, which suggests a potential route to mitigate photon loss.
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Affiliation(s)
- Haoyu Qi
- Xanadu, 777 Bay Street, Toronto, Ontario M5G 2C8, Canada
| | - Daniel J Brod
- Instituto de Física, Universidade Federal Fluminense, Niterói, Rio de Janeiro 24210-340, Brazil
| | | | - Raúl García-Patrón
- Centre for Quantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles, 1050 Brussels, Belgium
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Chabaud U, Markham D, Grosshans F. Stellar Representation of Non-Gaussian Quantum States. PHYSICAL REVIEW LETTERS 2020; 124:063605. [PMID: 32109095 DOI: 10.1103/physrevlett.124.063605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2019] [Accepted: 01/21/2020] [Indexed: 06/10/2023]
Abstract
The so-called stellar formalism allows us to represent the non-Gaussian properties of single-mode quantum states by the distribution of the zeros of their Husimi Q function in phase space. We use this representation in order to derive an infinite hierarchy of single-mode states based on the number of zeros of the Husimi Q function: the stellar hierarchy. We give an operational characterization of the states in this hierarchy with the minimal number of single-photon additions needed to engineer them, and derive equivalence classes under Gaussian unitary operations. We study in detail the topological properties of this hierarchy with respect to the trace norm, and discuss implications for non-Gaussian state engineering, and continuous variable quantum computing.
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Affiliation(s)
- Ulysse Chabaud
- Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
| | - Damian Markham
- Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
| | - Frédéric Grosshans
- Laboratoire d'Informatique de Paris 6, CNRS, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
- Laboratoire Aimé Cotton, CNRS, Université Paris-Sud, ENS Cachan, Université Paris-Saclay, 91405 Orsay Cedex
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Wang J, He J, Ma Y. Finite-time performance of a quantum heat engine with a squeezed thermal bath. Phys Rev E 2019; 100:052126. [PMID: 31870038 DOI: 10.1103/physreve.100.052126] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2019] [Indexed: 06/10/2023]
Abstract
We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures β_{h} and β_{c}(>β_{h}) with (k_{B}≡1)β=1/T. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as η_{mp}=(η_{C}^{gen})^{2}/[η_{C}^{gen}-(1-η_{C}^{gen})ln(1-η_{C}^{gen})], where the generalized Carnot efficiency η_{C}^{gen} in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter γ: η_{C}^{gen}=1-β_{h}/[β_{c}cosh(2γ)]. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.
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Affiliation(s)
- Jianhui Wang
- Department of Physics, Nanchang University, Nanchang 330031, China
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - Jizhou He
- Department of Physics, Nanchang University, Nanchang 330031, China
| | - Yongli Ma
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
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Bina M, Amelio I, Paris MGA. Dicke coupling by feasible local measurements at the superradiant quantum phase transition. Phys Rev E 2016; 93:052118. [PMID: 27300841 DOI: 10.1103/physreve.93.052118] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Indexed: 06/06/2023]
Abstract
We address characterization of many-body superradiant systems and establish a fundamental connection between quantum criticality and the possibility of locally estimating the coupling constant, i.e., extracting its value by probing only a portion of the whole system. In particular, we consider Dicke-like superradiant systems made of an ensemble of two-level atoms interacting with a single-mode radiation field at zero effective temperature, and address estimation of the coupling by measurements performed only on radiation. At first, we obtain analytically the quantum Fisher information (QFI) and show that optimal estimation of the coupling may be achieved by tuning the frequency of the radiation field to drive the system toward criticality. The scaling behavior of the QFI at the critical point is obtained explicitly upon exploiting the symplectic formalism for Gaussian states. We then analyze the performances of feasible detection schemes performed only on the radiation subsystem, namely homodyne detection and photon counting, and show that the corresponding Fisher informations (FIs) approach the global QFI in the critical region. We thus conclude that criticality is a twofold resource. On the one hand, global QFI diverges at the critical point, i.e., the coupling may be estimated with the arbitrary precision. On the other hand, the FIs of feasible local measurements (which are generally smaller than the QFI out of the critical region), show the same scaling of the global QFI; i.e., optimal estimation of coupling may be achieved by locally probing the system, despite its strongly interacting nature.
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Affiliation(s)
- M Bina
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano, Italy
| | - I Amelio
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano, Italy
| | - M G A Paris
- Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano, Italy; CNISM, UdR Milano Statale, I-20133 Milano, Italy; and INFN, Sezione di Milano, I-20133 Milano, Italy
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7
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Long R, Liu W. Performance of quantum Otto refrigerators with squeezing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062137. [PMID: 26172691 DOI: 10.1103/physreve.91.062137] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2014] [Indexed: 06/04/2023]
Abstract
The performance of a quantum Otto refrigerator coupled to a squeezed cold reservoir has been evaluated using the χ figure of merit. We have shown that squeezing can enhance the coefficient of performance (COP) dramatically, surpassing the Carnot COP defined by the initial temperatures of the heat baths. Furthermore, when the squeezing parameter approaches its maximum value, the work input vanishes while the cooling rate remains finite, in apparent contravention of the second law of thermodynamics. To explain this phenomenon, we have shown that squeezing renders the thermal bath into a nonequilibrium state and the temperature of the bath becomes frequency dependent. Thereby, a correlation to the Carnot COP has been deduced. The results reveal that the COP under the maximum χ figure of merit is of the Curzon-Ahlborn style that cannot surpass the actual Carnot COP, and is thus consistent with the second law of thermodynamics.
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Affiliation(s)
- Rui Long
- School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Wei Liu
- School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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Lo PY, Xiong HN, Zhang WM. Breakdown of Bose-Einstein distribution in photonic crystals. Sci Rep 2015; 5:9423. [PMID: 25822135 PMCID: PMC4378511 DOI: 10.1038/srep09423] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Accepted: 03/03/2015] [Indexed: 12/05/2022] Open
Abstract
In the last two decades, considerable advances have been made in the investigation of nano-photonics in photonic crystals. Previous theoretical investigations of photon dynamics were carried out at zero temperature. Here, we investigate micro/nano cavity photonics in photonic crystals at finite temperature. Due to photonic-band-gap-induced localized long-lived photon dynamics, we discover that cavity photons in photonic crystals do not obey Bose-Einstein statistical distribution. Within the photonic band gap and in the vicinity of the band edge, cavity photons combine the long-lived non-Markovain dynamics with thermal fluctuations together to form photon states that memorize the initial cavity state information. As a result, Bose-Einstein distribution is completely broken down in these regimes, even if the thermal energy is larger or much larger than the cavity detuning energy. In this investigation, a crossover phenomenon from equilibrium to nonequilibrium steady states is also revealed.
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Affiliation(s)
- Ping-Yuan Lo
- Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan, Republic of China
| | - Heng-Na Xiong
- Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan, Republic of China
| | - Wei-Min Zhang
- Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan, Republic of China
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Roßnagel J, Abah O, Schmidt-Kaler F, Singer K, Lutz E. Nanoscale heat engine beyond the Carnot limit. PHYSICAL REVIEW LETTERS 2014; 112:030602. [PMID: 24484127 DOI: 10.1103/physrevlett.112.030602] [Citation(s) in RCA: 184] [Impact Index Per Article: 18.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2013] [Indexed: 06/03/2023]
Abstract
We consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to a squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, surpassing the standard Carnot limit and approaching unity exponentially for large squeezing parameters. We further propose an experimental scheme to implement such a model system by using a single trapped ion in a linear Paul trap with special geometry. Our analytical investigations are supported by Monte Carlo simulations that demonstrate the feasibility of our proposal. For realistic trap parameters, an increase of the efficiency at maximum power of up to a factor of 4 is reached, largely exceeding the Carnot bound.
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Affiliation(s)
- J Roßnagel
- Quantum, Institut für Physik, Universität Mainz, D-55128 Mainz, Germany
| | - O Abah
- Institute for Theoretical Physics, University of Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - F Schmidt-Kaler
- Quantum, Institut für Physik, Universität Mainz, D-55128 Mainz, Germany
| | - K Singer
- Quantum, Institut für Physik, Universität Mainz, D-55128 Mainz, Germany
| | - E Lutz
- Institute for Theoretical Physics, University of Erlangen-Nürnberg, D-91058 Erlangen, Germany
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D'Auria V, Fornaro S, Porzio A, Solimeno S, Olivares S, Paris MGA. Full characterization of Gaussian bipartite entangled states by a single homodyne detector. PHYSICAL REVIEW LETTERS 2009; 102:020502. [PMID: 19257255 DOI: 10.1103/physrevlett.102.020502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2008] [Indexed: 05/27/2023]
Abstract
We present the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement, and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of optical parametric oscillator signals and represent a tool for quantum technology based on continuous variable entanglement.
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Affiliation(s)
- V D'Auria
- Dipartimento di Scienze Fisiche Università Federico II, Napoli, Italy
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D’Auria V, Porzio A, Solimeno S, Olivares S, Paris MGA. Characterization of bipartite states using a single homodyne detector. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/1464-4266/7/12/044] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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12
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Olivares S, Paris MGA. Binary optical communication in single-mode and entangled quantum noisy channels. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/1464-4266/6/1/012] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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13
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Marian P, Marian TA, Scutaru H. Quantifying nonclassicality of one-mode Gaussian states of the radiation field. PHYSICAL REVIEW LETTERS 2002; 88:153601. [PMID: 11955195 DOI: 10.1103/physrevlett.88.153601] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2001] [Indexed: 05/23/2023]
Abstract
We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.
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Affiliation(s)
- Paulina Marian
- Institute for Theoretical Atomic and Molecular Physics, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
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14
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Dodonov VV. `Nonclassical' states in quantum optics: a `squeezed' review of the first 75 years. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/1464-4266/4/1/201] [Citation(s) in RCA: 639] [Impact Index Per Article: 29.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Marian P, Marian TA, Scutaru H. Inseparability of mixed two-mode Gaussian states generated with aSU(1,1) interferometer. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/35/322] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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16
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Kim MS, Imoto N. Phase-sensitive reservoir modeled by beam splitters. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:2401-2410. [PMID: 9912501 DOI: 10.1103/physreva.52.2401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Musslimani ZH, Braunstein SL, Mann A, Revzen M. Destruction of photocount oscillations by thermal noise. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:4967-4973. [PMID: 9912190 DOI: 10.1103/physreva.51.4967] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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18
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Dodonov VV, Man'ko VI, Nikonov DE. Even and odd coherent states for multimode parametric systems. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:3328-3336. [PMID: 9911972 DOI: 10.1103/physreva.51.3328] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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19
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Vourdas A, Bishop RF. Thermal coherent states in the Bargmann representation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:3331-3339. [PMID: 9911281 DOI: 10.1103/physreva.50.3331] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Dodonov VV, Man'ko OV, Man'ko VI. Multidimensional Hermite polynomials and photon distribution for polymode mixed light. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:813-817. [PMID: 9910955 DOI: 10.1103/physreva.50.813] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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21
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Dodonov VV, Man'ko OV, Man'ko VI. Photon distribution for one-mode mixed light with a generic Gaussian Wigner function. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 49:2993-3001. [PMID: 9910582 DOI: 10.1103/physreva.49.2993] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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22
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Marian P, Marian TA. Squeezed states with thermal noise. II. Damping and photon counting. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:4487-4495. [PMID: 9909457 DOI: 10.1103/physreva.47.4487] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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