1
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Zhang ZZ, Tan QS, Wu W. Statistics of quantum heat in the Caldeira-Leggett model. Phys Rev E 2024; 109:064134. [PMID: 39021018 DOI: 10.1103/physreve.109.064134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2024] [Accepted: 06/03/2024] [Indexed: 07/20/2024]
Abstract
Nonequilibrium fluctuation relation lies at the heart of the quantum thermodynamics. Many previous studies have demonstrated that the heat exchange between a quantum system and a thermal bath initially prepared in their own Gibbs states at different temperatures obeys the famous Jarzynski-Wójcik fluctuation theorem. However, this conclusion is obtained under the assumption of Born-Markovian approximation. In this paper, going beyond the Born-Markovian limitation, we investigate the statistics of quantum heat in an exactly non-Markovian relaxation process described by the well-known Caldeira-Leggett model. It is revealed that the Jarzynski-Wójcik fluctuation theorem breaks down in the strongly non-Markovian regime. Moreover, we find the steady-state quantum heat within the non-Markovian framework can be widely tunable by using the quantum reservoir-engineering technique. These results are sharply contrary to the common Born-Markovian predictions. Our results presented in this paper may update the understanding of the quantum thermodynamics in strongly coupled and low-temperature systems. Moreover, the controllable heat may have some potential applications in improving the performance of a quantum heat engine.
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Affiliation(s)
- Ze-Zhou Zhang
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | | | - Wei Wu
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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2
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Jackson CS, Caves CM. Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1254. [PMID: 37761553 PMCID: PMC10529125 DOI: 10.3390/e25091254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Revised: 08/08/2023] [Accepted: 08/11/2023] [Indexed: 09/29/2023]
Abstract
We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument's evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups.
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Affiliation(s)
| | - Carlton M. Caves
- Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM 87131, USA
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3
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Zhang ZZ, Tan QS, Wu W. Heat distribution in quantum Brownian motion. Phys Rev E 2023; 108:014138. [PMID: 37583192 DOI: 10.1103/physreve.108.014138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2023] [Accepted: 07/11/2023] [Indexed: 08/17/2023]
Abstract
We investigate the heat statistics in a relaxation process of quantum Brownian motion described by the Caldeira-Leggett model. By employing the normal mode transformation and the phase-space formulation approach, we can analyze the quantum heat distribution within an exactly dynamical framework beyond the traditional paradigm of Born-Markovian and weak-coupling approximations. It is revealed that the exchange fluctuation theorem for quantum heat generally breaks down in the strongly non-Markovian regime. Our results may improve the understanding about the nonequilibrium thermodynamics of open quantum systems when the usual Markovian treatment is no longer appropriate.
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Affiliation(s)
- Ze-Zhou Zhang
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | - Qing-Shou Tan
- Key Laboratory of Hunan Province on Information Photonics and Freespace Optical Communication, College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414000, China
| | - Wei Wu
- Key Laboratory of Quantum Theory and Applications of Ministry of Education, Lanzhou University, Lanzhou 730000, China
- Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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4
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Cavaliere F, Razzoli L, Carrega M, Benenti G, Sassetti M. Hybrid quantum thermal machines with dynamical couplings. iScience 2023; 26:106235. [PMID: 36922994 PMCID: PMC10009053 DOI: 10.1016/j.isci.2023.106235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 01/31/2023] [Accepted: 02/15/2023] [Indexed: 02/22/2023] Open
Abstract
Quantum thermal machines can perform useful tasks, such as delivering power, cooling, or heating. In this work, we consider hybrid thermal machines, that can execute more than one task simultaneously. We characterize and find optimal working conditions for a three-terminal quantum thermal machine, where the working medium is a quantum harmonic oscillator, coupled to three heat baths, with two of the couplings driven periodically in time. We show that it is possible to operate the thermal machine efficiently, in both pure and hybrid modes, and to switch between different operational modes simply by changing the driving frequency. Moreover, the proposed setup can also be used as a high-performance transistor, in terms of output-to-input signal and differential gain. Owing to its versatility and tunability, our model may be of interest for engineering thermodynamic tasks and for thermal management in quantum technologies.
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Affiliation(s)
- Fabio Cavaliere
- Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy.,CNR-SPIN, Via Dodecaneso 33, 16146 Genova, Italy
| | - Luca Razzoli
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
| | | | - Giuliano Benenti
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy.,NEST, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Maura Sassetti
- Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy.,CNR-SPIN, Via Dodecaneso 33, 16146 Genova, Italy
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5
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Hsiang JT, Arısoy O, Hu BL. Entanglement Dynamics of Coupled Quantum Oscillators in Independent NonMarkovian Baths. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1814. [PMID: 36554219 PMCID: PMC9778547 DOI: 10.3390/e24121814] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Revised: 12/04/2022] [Accepted: 12/10/2022] [Indexed: 06/17/2023]
Abstract
This work strives to better understand how the entanglement in an open quantum system, here represented by two coupled Brownian oscillators, is affected by a nonMarkovian environment (with memories), here represented by two independent baths each oscillator separately interacts with. We consider two settings, a 'symmetric' configuration wherein the parameters of both oscillators and their baths are identical, and an 'asymmetric' configuration wherein they are different, in particular, a 'hybrid' configuration, where one of the two coupled oscillators interacts with a nonMarkovian bath and the other with a Markovian bath. Upon finding the solutions to the Langevin equations governing the system dynamics and the evolution of the covariance matrix elements entering into its entanglement dynamics, we ask two groups of questions: (Q1) Which time regime does the bath's nonMarkovianity benefit the system's entanglement most? The answers we get from detailed numerical studies suggest that (A1) For an initially entangled pair of oscillators, we see that in the intermediate time range, the duration of entanglement is proportional to the memory time, and it lasts a fraction of the relaxation time, but at late times when the dynamics reaches a steady state, the value of the symplectic eigenvalue of the partially transposed covariance matrix barely benefit from the bath nonMarkovianity. For the second group of questions: (Q2) Can the memory of one nonMarkovian bath be passed on to another Markovian bath? And if so, does this memory transfer help to sustain the system's entanglement dynamics? Our results from numerical studies of the asymmetric hybrid configuration indicate that (A2) A system with a short memory time can acquire improvement when it is coupled to another system with a long memory time, but, at a cost of the latter. The sustainability of the bipartite entanglement is determined by the party which breaks off entanglement most easily.
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Affiliation(s)
- Jen-Tsung Hsiang
- Center for High Energy and High Field Physics, National Central University, Taoyuan 320317, Taiwan
| | - Onat Arısoy
- Chemical Physics Program and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
| | - Bei-Lok Hu
- Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA
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6
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Becker T, Schnell A, Thingna J. Canonically Consistent Quantum Master Equation. PHYSICAL REVIEW LETTERS 2022; 129:200403. [PMID: 36461992 DOI: 10.1103/physrevlett.129.200403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Revised: 08/01/2022] [Accepted: 10/11/2022] [Indexed: 06/17/2023]
Abstract
We put forth a new class of quantum master equations that correctly reproduce the asymptotic state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics. The correction not only steers the reduced system toward a correct steady state but also improves the accuracy of the dynamics, thereby refining the archetypal Born-Markov weak-coupling second-order master equations. In case of equilibrium, we use the exact mean-force Gibbs state to correct the Redfield quantum master equation. By benchmarking it with the exact solution of the damped harmonic oscillator, we show that our method also helps correct the long-standing issue of positivity violation, albeit without complete positivity. Our method of a canonically consistent quantum master equation opens a new perspective in the theory of open quantum systems leading to a reduced density matrix accurate beyond the commonly used Redfield and Lindblad equations, while retaining the same conceptual and numerical complexity.
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Affiliation(s)
- Tobias Becker
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Alexander Schnell
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany
| | - Juzar Thingna
- Department of Physics and Applied Physics, University of Massachusetts, Lowell, Massachusetts 01854, USA
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
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7
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Han LP, Zou J, Li H, Shao B. Quantum Information Scrambling in Non-Markovian Open Quantum System. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1532. [PMID: 36359623 PMCID: PMC9689867 DOI: 10.3390/e24111532] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/18/2022] [Revised: 10/17/2022] [Accepted: 10/21/2022] [Indexed: 06/16/2023]
Abstract
In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.
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Affiliation(s)
- Li-Ping Han
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
- School of Science, Tianjin University of Technology, Tianjin 300384, China
| | - Jian Zou
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Hai Li
- School of Information and Electronic Engineering, Shandong Technology and Business University, Yantai 264005, China
| | - Bin Shao
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
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8
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Zurek WH. Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1520. [PMID: 36359613 PMCID: PMC9689795 DOI: 10.3390/e24111520] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Revised: 03/18/2022] [Accepted: 03/21/2022] [Indexed: 06/16/2023]
Abstract
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that-when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)-these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer's records. However, our "let quantum be quantum" approach poses questions absent in Bohr's Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply "too relative", and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born's rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection-environment-induced superselection)-are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the 'quantum theory of the classical' one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability-hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability-the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states-(ii) entanglement-assisted invariance or envariance-implies Born's rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool-reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness-to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons-composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.
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9
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Reiche D, Hsiang JT, Hu BL. Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation–Dissipation Inequalities. ENTROPY 2022; 24:e24081016. [PMID: 35892996 PMCID: PMC9394344 DOI: 10.3390/e24081016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 07/16/2022] [Accepted: 07/19/2022] [Indexed: 02/04/2023]
Abstract
Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper [Dong et al., Entropy 2022, 24, 870], we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.
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Affiliation(s)
- Daniel Reiche
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße15, 12489 Berlin, Germany
- Correspondence:
| | - Jen-Tsung Hsiang
- Center for High Energy and High Field Physics, National Central University, Taoyuan 320317, Taiwan;
| | - Bei-Lok Hu
- Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA;
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10
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Teklu B, Bina M, Paris MGA. Noisy propagation of Gaussian states in optical media with finite bandwidth. Sci Rep 2022; 12:11646. [PMID: 35804038 PMCID: PMC9270350 DOI: 10.1038/s41598-022-15865-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 06/30/2022] [Indexed: 11/10/2022] Open
Abstract
We address propagation and entanglement of Gaussian states in optical media characterised by nontrivial spectral densities. In particular, we consider environments with a finite bandwidth \documentclass[12pt]{minimal}
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\begin{document}$$J(\omega ) = J_0 \left[ \theta (\omega -\Omega ) - \theta (\omega - \Omega - \delta )\right] $$\end{document}J(ω)=J0θ(ω-Ω)-θ(ω-Ω-δ), and show that in the low temperature regime \documentclass[12pt]{minimal}
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\begin{document}$$T\ll \Omega ^{-1}$$\end{document}T≪Ω-1: (i) secular terms in the master equation may be neglected; (ii) attenuation (damping) is strongly suppressed; (iii) the overall diffusion process may be described as a Gaussian noise channel with variance depending only on the bandwidth. We find several regimes where propagation is not much detrimental and entanglement may be protected form decoherence.
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Affiliation(s)
- Berihu Teklu
- Department of Applied Mathematics and Sciences and Center for Cyber-Physical Systems (C2PS), Khalifa University, 127788, Abu Dhabi, United Arab Emirates
| | - Matteo Bina
- Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, 20133, Milan, Italy
| | - Matteo G A Paris
- Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, 20133, Milan, Italy. .,INFN-Sezione di Milano, 20133, Milan, Italy.
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11
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Dong H, Reiche D, Hsiang JT, Hu BL. Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations. ENTROPY 2022; 24:e24070870. [PMID: 35885093 PMCID: PMC9324490 DOI: 10.3390/e24070870] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Revised: 06/15/2022] [Accepted: 06/19/2022] [Indexed: 02/05/2023]
Abstract
Thermodynamic uncertainty principles make up one of the few rare anchors in the largely uncharted waters of nonequilibrium systems, the fluctuation theorems being the more familiar. In this work we aim to trace the uncertainties of thermodynamic quantities in nonequilibrium systems to their quantum origins, namely, to the quantum uncertainty principles. Our results enable us to make this categorical statement: For Gaussian systems, thermodynamic functions are functionals of the Robertson-Schrödinger uncertainty function, which is always non-negative for quantum systems, but not necessarily so for classical systems. Here, quantum refers to noncommutativity of the canonical operator pairs. From the nonequilibrium free energy, we succeeded in deriving several inequalities between certain thermodynamic quantities. They assume the same forms as those in conventional thermodynamics, but these are nonequilibrium in nature and they hold for all times and at strong coupling. In addition we show that a fluctuation-dissipation inequality exists at all times in the nonequilibrium dynamics of the system. For nonequilibrium systems which relax to an equilibrium state at late times, this fluctuation-dissipation inequality leads to the Robertson-Schrödinger uncertainty principle with the help of the Cauchy-Schwarz inequality. This work provides the microscopic quantum basis to certain important thermodynamic properties of macroscopic nonequilibrium systems.
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Affiliation(s)
- Hang Dong
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China;
| | - Daniel Reiche
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany;
| | - Jen-Tsung Hsiang
- Center for High Energy and High Field Physics, National Central University, Taoyuan 320317, Taiwan
- Correspondence:
| | - Bei-Lok Hu
- Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA;
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12
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Butera S. Influence functional for two mirrors interacting via radiation pressure. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.105.016023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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13
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Coupled Harmonic Oscillator in a System of Free Particles. MATHEMATICS 2022. [DOI: 10.3390/math10030294] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The coupled quantum harmonic oscillator is one of the most researched and important model systems in quantum optics and quantum informatics. This system is often investigated for quantum entanglement in the environment. As a result, such studies are complex and can only be carried out using numerical methods that do not reveal the general pattern of such systems. In this work, the external environment is considered to be two independent particles interacting with coupled harmonic oscillators. It is shown that such a system has an exact analytical solution to the dynamic Schrödinger equation. The analysis of this solution is carried out, and the main parameters of this system are revealed. The solutions obtained can be used to study more complex systems and their quantum entanglement.
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14
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Abstract
After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.
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15
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Arısoy O, Hsiang JT, Hu BL. Quantum-parametric-oscillator heat engines in squeezed thermal baths: Foundational theoretical issues. Phys Rev E 2022; 105:014108. [PMID: 35193212 DOI: 10.1103/physreve.105.014108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Accepted: 12/21/2021] [Indexed: 06/14/2023]
Abstract
In this paper we examine some foundational issues of a class of quantum engines where the system consists of a single quantum parametric oscillator, operating in an Otto cycle consisting of four stages of two alternating phases: the isentropic phase is detached from any bath (thus a closed system) where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system (now rendered open) is put in contact with one or two squeezed baths of different temperatures, whose nonequilibrium dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian motion. The HPZ equation is an exact non-Markovian equation which preserves the positivity of the density operator and is valid for (1) all temperatures, (2) arbitrary spectral density of the bath, and (3) arbitrary coupling strength between the system and the bath. Taking advantage of these properties we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. This includes (1) the non-Markovian regimes for non-Ohmic, low-temperature baths, (2) what to expect in nonadiabatic frequency modulations, (3) strong system-bath coupling, as well as (4) the proper junction conditions between these two phases. Our aim here is not to present ways for attaining higher efficiency but to build a more solid theoretical foundation for quantum engines of continuous variables covering a broader range of parameter spaces that we hope are of use for exploring such possibilities.
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Affiliation(s)
- Onat Arısoy
- Chemical Physics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Jen-Tsung Hsiang
- Center for High Energy and High Field Physics, National Central University, Taoyuan 320317, Taiwan, ROC
| | - Bei-Lok Hu
- Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA
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16
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Chen JF, Qiu T, Quan HT. Quantum-Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1602. [PMID: 34945908 PMCID: PMC8700725 DOI: 10.3390/e23121602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Revised: 11/22/2021] [Accepted: 11/23/2021] [Indexed: 11/17/2022]
Abstract
Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum-classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.
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Affiliation(s)
- Jin-Fu Chen
- School of Physics, Peking University, Beijing 100871, China; (J.-F.C.); (T.Q.)
| | - Tian Qiu
- School of Physics, Peking University, Beijing 100871, China; (J.-F.C.); (T.Q.)
| | - Hai-Tao Quan
- School of Physics, Peking University, Beijing 100871, China; (J.-F.C.); (T.Q.)
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, China
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17
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Chakraborty A, Sensarma R. Nonequilibrium Dynamics of Renyi Entropy for Bosonic Many-Particle Systems. PHYSICAL REVIEW LETTERS 2021; 127:200603. [PMID: 34860062 DOI: 10.1103/physrevlett.127.200603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Revised: 05/10/2021] [Accepted: 10/04/2021] [Indexed: 06/13/2023]
Abstract
We propose a new field theoretic method for calculating Renyi entropy of a subsystem of many interacting bosons without using replica methods. This method is applicable to dynamics of both open and closed quantum systems starting from arbitrary initial conditions. Our method identifies the Wigner characteristic of a reduced density matrix with the partition function of the whole system with a set of linear sources turned on only in the subsystem, and uses this to calculate the subsystem's Renyi entropy. We use this method to study the evolution of Renyi entropy in a noninteracting open quantum system starting from an initial Fock state. We find a relation between the initial state and final density matrix which determines whether the entropy shows nonmonotonic behavior in time. For non-Markovian dynamics, we show that the entropy approaches its steady-state value as a power law with exponents governed by nonanalyticities of the bath. We illustrate that this field-theoretic method can be used to study large bosonic open quantum systems.
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Affiliation(s)
- Ahana Chakraborty
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstrasse 38, 01187 Dresden, Germany
| | - Rajdeep Sensarma
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400005, India
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18
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Brian D, Sun X. Generalized quantum master equation: A tutorial review and recent advances. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2109157] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Dominikus Brian
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200241, China
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19
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Becker T, Wu LN, Eckardt A. Lindbladian approximation beyond ultraweak coupling. Phys Rev E 2021; 104:014110. [PMID: 34412241 DOI: 10.1103/physreve.104.014110] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Accepted: 06/08/2021] [Indexed: 11/07/2022]
Abstract
Away from equilibrium, the properties of open quantum systems depend on the details of their environment. A microscopic derivation of a master equation (ME) is therefore crucial. Of particular interest are Lindblad-type equations, not only because they provide the most general class of Markovian MEs, but also since they are the starting point for efficient quantum trajectory simulations. Lindblad-type MEs are commonly derived from the Born-Markov-Redfield equation via a rotating-wave approximation (RWA). However the RWA is valid only for ultraweak system-bath coupling and often fails to accurately describe nonequilibrium processes. Here we derive an alternative Lindbladian approximation to the Redfield equation, which does not rely on ultraweak system-bath coupling. Applying it to an extended Hubbard model coupled to Ohmic baths, we show that, especially away from equilibrium, it provides a good approximation in large parameter regimes where the RWA fails.
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Affiliation(s)
- Tobias Becker
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Ling-Na Wu
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - André Eckardt
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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20
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Reitz M, Genes C. Floquet engineering of molecular dynamics via infrared coupling. J Chem Phys 2020; 153:234305. [PMID: 33353327 DOI: 10.1063/5.0033382] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We discuss Floquet engineering of dissipative molecular systems through periodic driving of an infrared-active vibrational transition, either directly or via a cavity mode. Following a polaron quantum Langevin equation approach, we derive correlation functions and stationary quantities showing strongly modified optical response of the infrared-dressed molecule. The coherent excitation of molecular vibrational modes in combination with the modulation of electronic degrees of freedom due to vibronic coupling can lead to both enhanced vibronic coherence and control over vibrational sideband amplitudes. The additional coupling to an infrared cavity allows for the controlled suppression of undesired sidebands, an effect stemming from the Purcell enhancement of vibrational relaxation rates.
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Affiliation(s)
- Michael Reitz
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
| | - Claudiu Genes
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
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21
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Excitation Dynamics in Chain-Mapped Environments. ENTROPY 2020; 22:e22111320. [PMID: 33287085 PMCID: PMC7712952 DOI: 10.3390/e22111320] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Revised: 11/13/2020] [Accepted: 11/17/2020] [Indexed: 11/17/2022]
Abstract
The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.
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22
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Gong H, Wang Y, Zhang HD, Qiao Q, Xu RX, Zheng X, Yan Y. Equilibrium and transient thermodynamics: A unified dissipaton-space approach. J Chem Phys 2020; 153:154111. [PMID: 33092348 DOI: 10.1063/5.0021203] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work presents a unified dissipaton-equation-of-motion (DEOM) theory and its evaluations on the Helmholtz free energy change due to the isotherm mixing of two isolated subsystems. One is a local impurity, and the other is a nonlocal Gaussian bath. DEOM constitutes a fundamental theory for such open quantum mixtures. To complete the theory, we also construct the imaginary-time DEOM formalism via an analytical continuation of dissipaton algebra, which would be limited to equilibrium thermodynamics. On the other hand, the real-time DEOM deals with both equilibrium structural and nonequilibrium dynamic properties. Its combination with the thermodynamic integral formalism would be a viable and accurate means to both equilibrium and transient thermodynamics. As illustrations, we report the numerical results on a spin-boson system, with elaborations on the underlying anharmonic features, the thermodynamic entropy vs the von Neumann entropy, and an indication of "solvent-cage" formation. Beside the required asymptotic equilibrium properties, the proposed transient thermodynamics also supports the basic spontaneity criterion.
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Affiliation(s)
- Hong Gong
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hou-Dao Zhang
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qin Qiao
- Digital Medical Research Center of School of Basic Medical Sciences, Fudan University, Shanghai 200032, China
| | - Rui-Xue Xu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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23
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Ali MM, Huang WM, Zhang WM. Quantum thermodynamics of single particle systems. Sci Rep 2020; 10:13500. [PMID: 32782281 PMCID: PMC7419543 DOI: 10.1038/s41598-020-70450-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2020] [Accepted: 06/30/2020] [Indexed: 11/24/2022] Open
Abstract
Thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two-level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system-reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system-reservoir coupling regime where the Born-Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non-Markovian memory effect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by inflationary dynamics associated with negative dynamical temperature. The corresponding dynamical criticality provides a border separating classical and quantum worlds. The inflationary dynamics may also relate to the origin of big bang and universe inflation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved.
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Affiliation(s)
- Md Manirul Ali
- Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Wei-Ming Huang
- Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Wei-Min Zhang
- Department of Physics, National Cheng Kung University, Tainan, 70101, Taiwan.
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24
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Hsiang JT, Hu BL. Nonequilibrium nonlinear open quantum systems: Functional perturbative analysis of a weakly anharmonic oscillator. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.101.125002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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25
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Hovhannisyan AA, Sargsyan VV, Adamian GG, Antonenko NV, Lacroix D. Non-Markovian dynamics of quantum systems coupled with several mixed fermionic-bosonic heat baths. Phys Rev E 2020; 101:062115. [PMID: 32688609 DOI: 10.1103/physreve.101.062115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Accepted: 05/14/2020] [Indexed: 06/11/2023]
Abstract
For the fermionic or bosonic oscillator fully coupled to several heat baths with mixed statistics, the analytical expressions for the occupation numbers are derived within the non-Markovian quantum Langevin approach. Employing two or three heat baths and the Ohmic dissipation with Lorenzian cutoffs, the role of statistics of the system and heat baths in the dynamics of the system is studied.
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Affiliation(s)
- A A Hovhannisyan
- Joint Institute for Nuclear Research, 141980 Dubna, Russia
- Institute of Applied Problems of Physics, 0014 Yerevan, Armenia
- Quantum Computing Laboratory, 1142 Norakert, Armenia
| | - V V Sargsyan
- Joint Institute for Nuclear Research, 141980 Dubna, Russia
| | - G G Adamian
- Joint Institute for Nuclear Research, 141980 Dubna, Russia
| | - N V Antonenko
- Joint Institute for Nuclear Research, 141980 Dubna, Russia
- Tomsk Polytechnic University, 634050 Tomsk, Russia
| | - D Lacroix
- Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud,Université Paris-Saclay, F-91406 Orsay Cedex, France
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26
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Dynamical and thermodynamical approaches to open quantum systems. Sci Rep 2020; 10:2607. [PMID: 32054893 PMCID: PMC7018693 DOI: 10.1038/s41598-020-59241-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Accepted: 01/08/2020] [Indexed: 12/02/2022] Open
Abstract
The non-Markovian dynamics of open quantum systems is studied from two different points of view. The first one coincides with the traditional tracing out of the environmental degrees of freedom, presented in classical textbooks on open quantum systems. The second one is an approximation of the exact density operator with the knowledge of only several dynamical variables in the spirit of non-equilibrium thermodynamics. The approximation is based on the principle of maximal entropy. We discuss the information and the Renyi entropies, which lead to different approximations. The time-convolutionless master equation governs the dynamics of both traditional and approximated reduced density operator with a particular projection operator. Considering the example of two interacting qubits in a thermal environment, we compare the traditional and thermodynamical approaches.
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27
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Wang S, Ma XS, Cheng MT. Multipartite Entanglement Generation in a Structured Environment. ENTROPY 2020; 22:e22020191. [PMID: 33285966 PMCID: PMC7516616 DOI: 10.3390/e22020191] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Revised: 02/01/2020] [Accepted: 02/05/2020] [Indexed: 12/02/2022]
Abstract
In this paper, we investigate the entanglement generation of n-qubit states in a model consisting of n independent qubits, each coupled to a harmonic oscillator which is in turn coupled to a bath of N additional harmonic oscillators with nearest-neighbor coupling. With analysis, we can find that the steady multipartite entanglement with different values can be generated after a long-time evolution for different sizes of the quantum system. Under weak coupling between the system and the harmonic oscillator, multipartite entanglement can monotonically increase from zero to a stable value. Under strong coupling, multipartite entanglement generation shows a speed-up increase accompanied by some oscillations as non-Markovian behavior. Our results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance non-Markovian dynamics and make it take a very long time for the entanglement to reach a stable value. Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation. Finally, the entanglement generation of the additional harmonic oscillators is also discussed.
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28
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Sinha K, Meystre P, Goldschmidt EA, Fatemi FK, Rolston SL, Solano P. Non-Markovian Collective Emission from Macroscopically Separated Emitters. PHYSICAL REVIEW LETTERS 2020; 124:043603. [PMID: 32058765 DOI: 10.1103/physrevlett.124.043603] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2019] [Indexed: 06/10/2023]
Abstract
We study the collective radiative decay of a system of two two-level emitters coupled to a one-dimensional waveguide in a regime where their separation is comparable to the coherence length of a spontaneously emitted photon. The electromagnetic field propagating in the cavity-like geometry formed by the emitters exerts a retarded backaction on the system leading to strongly non-Markovian dynamics. The collective spontaneous emission rate of the emitters exhibits an enhancement or inhibition beyond the usual Dicke superradiance and subradiance due to self-consistent coherent time-delayed feedback.
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Affiliation(s)
- Kanupriya Sinha
- U.S. Army Research Laboratory, Adelphi, Maryland 20783, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| | - Pierre Meystre
- Department of Physics and College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | | | | | - S L Rolston
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Pablo Solano
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Maryland 02139, USA
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29
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Rubio López AE, Romero-Isart O. Radiation Reaction of a Jiggling Dipole in a Quantum Electromagnetic Field. PHYSICAL REVIEW LETTERS 2019; 123:243603. [PMID: 31922863 DOI: 10.1103/physrevlett.123.243603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2019] [Revised: 09/24/2019] [Indexed: 06/10/2023]
Abstract
We show how to derive a consistent quantum theory of radiation reaction of a nonrelativistic point-dipole quantum oscillator by including the dynamical fluctuations of the position of the dipole. The proposed nonlinear theory displays neither runaway solutions nor acausal behavior without requiring additional assumptions. Furthermore, we show that quantum (zero-point) fluctuations of the electromagnetic field are necessary to satisfy the second law of thermodynamics. Our results are obtained by developing a nonperturbative technique involving a weak-coupling approximation at the level of the effective action.
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Affiliation(s)
- Adrián E Rubio López
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Technikerstraße 21a, Innsbruck 6020, Austria and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
| | - Oriol Romero-Isart
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Technikerstraße 21a, Innsbruck 6020, Austria and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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30
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Goldwater D, Barker PF, Bassi A, Donadi S. Quantum Spectrometry for Arbitrary Noise. PHYSICAL REVIEW LETTERS 2019; 123:230801. [PMID: 31868443 DOI: 10.1103/physrevlett.123.230801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Indexed: 06/10/2023]
Abstract
We present a technique for recovering the spectrum of a non-Markovian bosonic bath and/or non-Markovian noises coupled to a harmonic oscillator. The treatment is valid under the conditions that the environment is large and hot compared to the oscillator, and that its temporal autocorrelation functions are symmetric with respect to time translation and reflection-criteria which we consider fairly minimal. We model a demonstration of the technique as deployed in the experimental scenario of a nanosphere levitated in a Paul trap, and show that it would effectively probe the spectrum of an electric field noise source from 10^{2} to 10^{6} Hz with a resolution inversely proportional to the measurement time. This technique may be deployed in quantum sensing, metrology, computing, and in experimental probes of foundational questions.
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Affiliation(s)
- Daniel Goldwater
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - P F Barker
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Angelo Bassi
- Department of Physics, University of Trieste, Strada Costiera 11, 34151 Trieste, Italy and Istituto Nazionale di Fisica Nucleare, Trieste Section, Via Valerio 2, 34127 Trieste, Italy
| | - Sandro Donadi
- Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany
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31
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Correa LA, Xu B, Morris B, Adesso G. Pushing the limits of the reaction-coordinate mapping. J Chem Phys 2019; 151:094107. [PMID: 31492070 DOI: 10.1063/1.5114690] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
The reaction-coordinate mapping is a useful technique to study complex quantum dissipative dynamics into structured environments. In essence, it aims to mimic the original problem by means of an "augmented system," which includes a suitably chosen collective environmental coordinate-the "reaction coordinate." This composite then couples to a simpler "residual reservoir" with short-lived correlations. If, in addition, the residual coupling is weak, a simple quantum master equation can be rigorously applied to the augmented system, and the solution of the original problem just follows from tracing out the reaction coordinate. But, what if the residual dissipation is strong? Here, we consider an exactly solvable model for heat transport-a two-node linear "quantum wire" connecting two baths at different temperatures. We allow for a structured spectral density at the interface with one of the reservoirs and perform the reaction-coordinate mapping, writing a perturbative master equation for the augmented system. We find that (a) strikingly, the stationary state of the original problem can be reproduced accurately by a weak-coupling treatment even when the residual dissipation on the augmented system is very strong, (b) the agreement holds throughout the entire dynamics under large residual dissipation in the overdamped regime; and (c) such a master equation can grossly overestimate the stationary heat current across the wire, even when its nonequilibrium steady state is captured faithfully. These observations can be crucial when using the reaction-coordinate mapping to study the largely unexplored strong-coupling regime in quantum thermodynamics.
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Affiliation(s)
- Luis A Correa
- CEMPS, Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom
| | - Buqing Xu
- School of Mathematical Sciences and CQNE, University of Nottingham, University Park Campus, Nottingham NG7 2RD, United Kingdom
| | - Benjamin Morris
- School of Mathematical Sciences and CQNE, University of Nottingham, University Park Campus, Nottingham NG7 2RD, United Kingdom
| | - Gerardo Adesso
- School of Mathematical Sciences and CQNE, University of Nottingham, University Park Campus, Nottingham NG7 2RD, United Kingdom
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32
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Tamascelli D, Smirne A, Lim J, Huelga SF, Plenio MB. Efficient Simulation of Finite-Temperature Open Quantum Systems. PHYSICAL REVIEW LETTERS 2019; 123:090402. [PMID: 31524443 DOI: 10.1103/physrevlett.123.090402] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2018] [Indexed: 06/10/2023]
Abstract
Chain-mapping techniques in combination with the time-dependent density matrix renormalization group are a powerful tool for the simulation of open-system quantum dynamics. For finite-temperature environments, however, this approach suffers from an unfavorable algorithmic scaling with increasing temperature. We prove that the system dynamics under thermal environments can be nonperturbatively described by temperature-dependent system-environmental couplings with the initial environment state being in its pure vacuum state, instead of a mixed thermal state. As a consequence, as long as the initial system state is pure, the global system-environment state remains pure at all times. The resulting speed-up and relaxed memory requirements of this approach enable the efficient simulation of open quantum systems interacting with highly structured environments in any temperature range, with applications extending from quantum thermodynamics to quantum effects in mesoscopic systems.
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Affiliation(s)
- D Tamascelli
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy
| | - A Smirne
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
| | - J Lim
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
| | - S F Huelga
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
| | - M B Plenio
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, 89069 Ulm, Germany
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33
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Moreno C, Urbina JD. Strong coupling and non-Markovian effects in the statistical notion of temperature. Phys Rev E 2019; 99:062135. [PMID: 31330588 DOI: 10.1103/physreve.99.062135] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Indexed: 11/07/2022]
Abstract
We investigate the emergence of temperature T in the system-plus-reservoir paradigm starting from the fundamental microcanonical scenario at total fixed energy E where, contrary to the canonical approach, T=T(E) is not a control parameter but a derived auxiliary concept. As shown by Schwinger for the regime of weak coupling γ between subsystems, T(E) emerges from the saddle-point analysis leading to the ensemble equivalence up to corrections O(1/sqrt[N]) in the number of particles N that defines the thermodynamic limit. By extending these ideas for finite γ, while keeping N→∞, we provide a consistent generalization of temperature T(E,γ) in strongly coupled systems, and we illustrate its main features for the specific model of quantum Brownian motion where it leads to consistent microcanonical thermodynamics. Interestingly, while this T(E,γ) is a monotonically increasing function of the total energy E, its dependence with γ is a purely quantum effect notably visible near the ground-state energy and for large energies differs for Markovian and non-Markovian regimes.
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Affiliation(s)
- Camilo Moreno
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Juan-Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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34
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Abstract
A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.
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Affiliation(s)
- Ronnie Kosloff
- The Institute of Chemistry and The Fritz Haber Centre for Theoretical Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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35
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Reitz M, Sommer C, Genes C. Langevin Approach to Quantum Optics with Molecules. PHYSICAL REVIEW LETTERS 2019; 122:203602. [PMID: 31172783 DOI: 10.1103/physrevlett.122.203602] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2019] [Indexed: 05/20/2023]
Abstract
We investigate the interaction between light and molecular systems modeled as quantum emitters coupled to a multitude of vibrational modes via a Holstein-type interaction. We follow a quantum Langevin equations approach that allows for analytical derivations of absorption and fluorescence profiles of molecules driven by classical fields or coupled to quantized optical modes. We retrieve analytical expressions for the modification of the radiative emission branching ratio in the Purcell regime and for the asymmetric cavity transmission associated with dissipative cross talk between upper and lower polaritons in the strong coupling regime. We also characterize the Förster resonance energy transfer process between donor-acceptor molecules mediated by the vacuum or by a cavity mode.
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Affiliation(s)
- Michael Reitz
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
| | - Christian Sommer
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
| | - Claudiu Genes
- Max Planck Institute for the Science of Light, Staudtstraße 2, D-91058 Erlangen, Germany
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36
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Elouard C, Besga B, Auffèves A. Probing the State of a Mechanical Oscillator with an Ultrastrongly Coupled Quantum Emitter. PHYSICAL REVIEW LETTERS 2019; 122:013602. [PMID: 31012721 DOI: 10.1103/physrevlett.122.013602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Indexed: 06/09/2023]
Abstract
Performing accurate position measurements of a mechanical resonator by coupling it to some optically driven quantum emitter is an important challenge for quantum sensing and metrology. We fully characterize the quantum noise associated with this measurement process, by deriving master equations for the coupled emitter and the resonator valid in the ultrastrong coupling regime. At short timescales, we show that this noise sets a fundamental limit to the readout sensitivity and that the standard quantum limit can be recovered for realistic experimental conditions. At long timescales, the scattering of the mechanical quadratures leads to the decoupling of the emitter from the driving light, switching off the noise source. This method can be used to describe the interaction of any quantum system strongly coupled to a finite size reservoir.
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Affiliation(s)
- Cyril Elouard
- Department of Physics and Astronomy and Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
| | - Benjamin Besga
- Université de Lyon, CNRS, Laboratoire de Physique de l'École Normale Supérieure, UMR5672, 46 Allée d'Italie, 69364 Lyon, France
| | - Alexia Auffèves
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
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37
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Xiong B, Li X, Chao SL, Zhou L. Optomechanical quadrature squeezing in the non-Markovian regime. OPTICS LETTERS 2018; 43:6053-6056. [PMID: 30548003 DOI: 10.1364/ol.43.006053] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Accepted: 11/14/2018] [Indexed: 06/09/2023]
Abstract
Squeezing of quantum fluctuation plays an important role in fundamental quantum physics and has marked influence on ultrasensitive detection. We propose a scheme to generate and enhance the squeezing of mechanical mode by exposing the optomechanical system to a non-Markovian environment. It is shown that the effective parametric resonance term of mechanical mode can be induced due to interaction with the cavity and non-Markovian reservoir, thus resulting in quadrature squeezing of the mechanical resonator; jointing the two kinds of interactions can enhance the squeezing effect. Compared with the usual Markovian regime, we can obtain stronger squeezing, and, significantly, the squeezing can approach a low asymptotic stable value.
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38
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Bialas P, Spiechowicz J, Łuczka J. Partition of energy for a dissipative quantum oscillator. Sci Rep 2018; 8:16080. [PMID: 30382144 PMCID: PMC6208383 DOI: 10.1038/s41598-018-34385-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2018] [Accepted: 10/18/2018] [Indexed: 11/26/2022] Open
Abstract
We reveal a new face of the old clichéd system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems. Both mean kinetic energy Ek and mean potential energy Ep of the oscillator are expressed as Ek = 〈εk〉 and Ep = 〈εp〉, where 〈εk〉 and 〈εp〉 are mean kinetic and potential energies per one degree of freedom of the thermostat which consists of harmonic oscillators too. The symbol 〈...〉 denotes two-fold averaging: (i) over the Gibbs canonical state for the thermostat and (ii) over thermostat oscillators frequencies ω which contribute to Ek and Ep according to the probability distribution [Formula: see text] and [Formula: see text], respectively. The role of the system-thermostat coupling strength and the memory time is analysed for the exponentially decaying memory function (Drude dissipation mechanism) and the algebraically decaying damping kernel.
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Affiliation(s)
- P Bialas
- Institute of Physics and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500, Chorzów, Poland
| | - J Spiechowicz
- Institute of Physics and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500, Chorzów, Poland
- Institute of Physics, University of Augsburg, D-86135, Augsburg, Germany
| | - J Łuczka
- Institute of Physics and Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500, Chorzów, Poland.
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39
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Liu Y, Xu RX, Zhang HD, Yan Y. Dissipaton equation of motion theory versus Fokker-Planck quantum master equation. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1804083] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Yang Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei 230026, China
| | - Rui-xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei 230026, China
| | - Hou-dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), University of Science and Technology of China, Hefei 230026, China
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40
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Hovhannisyan AA, Sargsyan VV, Adamian GG, Antonenko NV, Lacroix D. Non-Markovian dynamics of fermionic and bosonic systems coupled to several heat baths. Phys Rev E 2018; 97:032134. [PMID: 29776062 DOI: 10.1103/physreve.97.032134] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2017] [Indexed: 11/07/2022]
Abstract
Employing the fermionic and bosonic Hamiltonians for the collective oscillator linearly FC-coupled with several heat baths, the analytical expressions for the collective occupation number are derived within the non-Markovian quantum Langevin approach. The master equations for the occupation number of collective subsystem are derived and discussed. In the case of Ohmic dissipation with Lorenzian cutoffs, the possibility of reduction of the system with several heat baths to the system with one heat bath is analytically demonstrated. For the fermionic and bosonic systems, a comparative analysis is performed between the collective subsystem coupled to two heat baths and the reference case of the subsystem coupled to one bath.
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Affiliation(s)
- A A Hovhannisyan
- Joint Institute for Nuclear Research, 141980 Dubna, Russia.,Physics Department, Yerevan State University, 0001-0099 Yerevan, Armenia
| | - V V Sargsyan
- Joint Institute for Nuclear Research, 141980 Dubna, Russia.,Institut für Theoretische Physik der Justus-Liebig-Universität, D-35392 Giessen, Germany
| | - G G Adamian
- Joint Institute for Nuclear Research, 141980 Dubna, Russia
| | - N V Antonenko
- Joint Institute for Nuclear Research, 141980 Dubna, Russia.,Mathematical Physics Department, Tomsk Polytechnic University, 634050 Tomsk, Russia
| | - D Lacroix
- Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, F-91406 Orsay Cedex, France
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41
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Jeknić-Dugić J, Petrović I, Arsenijević M, Dugić M. Dynamical stability of the one-dimensional rigid Brownian rotator: the role of the rotator's spatial size and shape. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:195304. [PMID: 29583124 DOI: 10.1088/1361-648x/aab9ef] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We investigate dynamical stability of a single propeller-like shaped molecular cogwheel modelled as the fixed-axis rigid rotator. In the realistic situations, rotation of the finite-size cogwheel is subject to the environmentally-induced Brownian-motion effect that we describe by utilizing the quantum Caldeira-Leggett master equation. Assuming the initially narrow (classical-like) standard deviations for the angle and the angular momentum of the rotator, we investigate the dynamics of the first and second moments depending on the size, i.e. on the number of blades of both the free rotator as well as of the rotator in the external harmonic field. The larger the standard deviations, the less stable (i.e. less predictable) rotation. We detect the absence of the simple and straightforward rules for utilizing the rotator's stability. Instead, a number of the size-related criteria appear whose combinations may provide the optimal rules for the rotator dynamical stability and possibly control. In the realistic situations, the quantum-mechanical corrections, albeit individually small, may effectively prove non-negligible, and also revealing subtlety of the transition from the quantum to the classical dynamics of the rotator. As to the latter, we detect a strong size-dependence of the transition to the classical dynamics beyond the quantum decoherence process.
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Affiliation(s)
- Jasmina Jeknić-Dugić
- University of Niš, Faculty of Science and Mathematics, Višegradska 33, 18000 Niš, Serbia
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42
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Colmenares PJ. Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics. Phys Rev E 2018; 97:052126. [PMID: 29906902 DOI: 10.1103/physreve.97.052126] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2017] [Indexed: 06/08/2023]
Abstract
This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.
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Affiliation(s)
- Pedro J Colmenares
- Departamento de Química, Universidad de Los Andes, Mérida 5101, Venezuela
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43
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Hsiang JT, Chou CH, Subaşı Y, Hu BL. Quantum thermodynamics from the nonequilibrium dynamics of open systems: Energy, heat capacity, and the third law. Phys Rev E 2018; 97:012135. [PMID: 29448480 DOI: 10.1103/physreve.97.012135] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Indexed: 11/07/2022]
Abstract
In a series of papers, we intend to take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations, and the laws of thermodynamics become well defined and viable for quantum many-body systems. We first describe how an open-system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. The linkage between the two comes from the reduced density matrix of ONEq in that stage having the same form as that of the system in the CGTs. We see the open-system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence, it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of N strongly coupled harmonic oscillators, interacting strongly with a scalar-field environment. In this paper, we focus on the internal energy, heat capacity, and the third law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity, and the validity of the third law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the third law of thermodynamics relies on quantum entanglement. They are conceptually and factually unrelated issues. Entropy and entanglement will be the main theme of our second paper on this subject matter.
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Affiliation(s)
- J-T Hsiang
- Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China
| | - C H Chou
- Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan
| | - Y Subaşı
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - B L Hu
- Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China.,Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
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44
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Gasbarri G, Toroš M, Bassi A. General Galilei Covariant Gaussian Maps. PHYSICAL REVIEW LETTERS 2017; 119:100403. [PMID: 28949182 DOI: 10.1103/physrevlett.119.100403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2017] [Indexed: 06/07/2023]
Abstract
We characterize general non-Markovian Gaussian maps which are covariant under Galilean transformations. In particular, we consider translational and Galilean covariant maps and show that they reduce to the known Holevo result in the Markovian limit. We apply the results to discuss measures of macroscopicity based on classicalization maps, specifically addressing dissipation, Galilean covariance and non-Markovianity. We further suggest a possible generalization of the macroscopicity measure defined by Nimmrichter and Hornberger [Phys. Rev. Lett. 110, 16 (2013)PRLTAO0031-9007].
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Affiliation(s)
- Giulio Gasbarri
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- Department of Physics, University of Trieste, Strada Costiera 11, 34151 Trieste, Italy
- Istituto Nazionale di Fisica Nucleare, Trieste Section, Via Valerio 2, 34127 Trieste, Italy
| | - Marko Toroš
- Department of Physics, University of Trieste, Strada Costiera 11, 34151 Trieste, Italy
- Istituto Nazionale di Fisica Nucleare, Trieste Section, Via Valerio 2, 34127 Trieste, Italy
| | - Angelo Bassi
- Department of Physics, University of Trieste, Strada Costiera 11, 34151 Trieste, Italy
- Istituto Nazionale di Fisica Nucleare, Trieste Section, Via Valerio 2, 34127 Trieste, Italy
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45
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Semin V. Exact dynamics of a two-level atom beyond the rotating wave approximation. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201716102023] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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Solution of the Master Equation for Quantum Brownian Motion Given by the Schrödinger Equation. MATHEMATICS 2016. [DOI: 10.3390/math5010001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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47
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Jang S. Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition. J Chem Phys 2016; 144:214102. [PMID: 27276940 DOI: 10.1063/1.4952477] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.
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Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics, and Initiative for Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
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48
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Bondar DI, Cabrera R, Campos A, Mukamel S, Rabitz HA. Wigner-Lindblad Equations for Quantum Friction. J Phys Chem Lett 2016; 7:1632-1637. [PMID: 27078510 DOI: 10.1021/acs.jpclett.6b00498] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.
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Affiliation(s)
- Denys I Bondar
- Princeton University , Princeton, New Jersey 08544, United States
| | - Renan Cabrera
- Princeton University , Princeton, New Jersey 08544, United States
| | - Andre Campos
- Princeton University , Princeton, New Jersey 08544, United States
| | - Shaul Mukamel
- University of California , Irvine, California 92697, United States
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49
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50
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Ferialdi L. Exact Closed Master Equation for Gaussian Non-Markovian Dynamics. PHYSICAL REVIEW LETTERS 2016; 116:120402. [PMID: 27058061 DOI: 10.1103/physrevlett.116.120402] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Indexed: 06/05/2023]
Abstract
Non-Markovian master equations describe general open quantum systems when no approximation is made. We provide the exact closed master equation for the class of Gaussian, completely positive, trace preserving, non-Markovian dynamics. This very general result allows us to investigate a vast variety of physical systems. We show that the master equation for non-Markovian quantum Brownian motion is a particular case of our general result. Furthermore, we derive the master equation unraveled by a non-Markovian, dissipative stochastic Schrödinger equation, paving the way for the analysis of dissipative non-Markovian collapse models.
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Affiliation(s)
- L Ferialdi
- Mathematisches Institut, Ludwig-Maximilians Universität, Theresienstraße 39, 80333 Munich, Germany
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