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Meng X, Sun Y, Wang Q, Ren J, Cai X, Czerwinski A. Dephasing Dynamics in a Non-Equilibrium Fluctuating Environment. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25040634. [PMID: 37190422 PMCID: PMC10137637 DOI: 10.3390/e25040634] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Revised: 04/05/2023] [Accepted: 04/07/2023] [Indexed: 05/17/2023]
Abstract
We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, of which the statistical properties are both non-stationary and non-Markovian. Due to the time-homogeneous property in the master equations for the multi-time probability distribution, the decoherence factor induced by the generalized RTN with a modulatable-type memory kernel can be exactly derived by means of a closed fourth-order differential equation with respect to time. In some special limit cases, the decoherence factor recovers to the expression of the previous ones. We analyzed in detail the environmental effect of memory modulation in the dynamical dephasing in four types of dynamics regimes. The results showed that the dynamical dephasing of the quantum system and the conversion between the Markovian and non-Markovian characters in the dephasing dynamics under the influence of the generalized RTN can be effectively modulated via the environmental memory kernel.
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Affiliation(s)
- Xiangjia Meng
- School of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China
- New Technology Research and Development Center of Intelligent Information Controlling in Universities of Shandong, Shandong Youth University of Political Science, Jinan 250103, China
| | - Yaxin Sun
- School of Science, Shandong Jianzhu University, Jinan 250101, China
| | - Qinglong Wang
- School of Science, Shandong Jianzhu University, Jinan 250101, China
| | - Jing Ren
- School of Science, Shandong Jianzhu University, Jinan 250101, China
| | - Xiangji Cai
- School of Science, Shandong Jianzhu University, Jinan 250101, China
| | - Artur Czerwinski
- Institute of Physics, Faculty of Physics, Astronomy and Intypeatics, Nicolaus Copernicus University in Torun, ul. Grudziadzka 5, 87-100 Torun, Poland
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Chen M, Chen H, Han T, Cai X. Disentanglement Dynamics in Nonequilibrium Environments. ENTROPY 2022; 24:1330. [PMCID: PMC9601490 DOI: 10.3390/e24101330] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 09/17/2022] [Indexed: 05/28/2023]
Abstract
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.
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Quantum nonlinear spectroscopy of single nuclear spins. Nat Commun 2022; 13:5318. [PMID: 36085280 PMCID: PMC9463177 DOI: 10.1038/s41467-022-32610-8] [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: 10/18/2021] [Accepted: 08/04/2022] [Indexed: 11/30/2022] Open
Abstract
Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics. Signals that look the same from their low-order correlations can often be distinguished by looking at higher-order ones. Here, the authors exploit the sensitivity of quantum nonlinear spectroscopy to fourth-order correlations to identify Gaussian noises, random-phased AC fields, and quantum spins.
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Budini AA, McHardy I, Nizama M, Cáceres MO. Emergence of stationary multimodality under two-timescaled dichotomic noise. Phys Rev E 2020; 101:052137. [PMID: 32575231 DOI: 10.1103/physreve.101.052137] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Accepted: 05/06/2020] [Indexed: 11/07/2022]
Abstract
We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic noise. It is shown that when the statistics of the time intervals between noise transitions is characterized by two well differentiated timescales, the stationary distribution may develop multimodality (bi- and trimodality). The underlying effects that lead to a probability concentration in different points include intermittence and also a dynamical locking of realizations. Our results are supported by numerical simulations as well as by an exact treatment obtained from a Markovian embedding of the full dynamics, which leads to a third-order differential equation for the stationary distribution.
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Affiliation(s)
- Adrián A Budini
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro Atómico Bariloche, Avenida E. Bustillo Km 9.5, (8400) Bariloche, Argentina and Universidad Tecnológica Nacional (UTN-FRBA), Fanny Newbery 111, (8400) Bariloche, Argentina
| | - Isaias McHardy
- Fellowship CONICET, Centro Atómico Bariloche, 8400 Bariloche, Argentina
| | - Marco Nizama
- Departamento de Física, Universidad Nacional del Comahue and CONICET, 8300 Neuquen, Argentina
| | - Manuel O Cáceres
- Centro Atómico Bariloche, CNEA, Instituto Balseiro, Universidad Nacional de Cuyo, and CONICET, 8400 Bariloche, Argentina
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Cai X. Quantum dephasing induced by non-Markovian random telegraph noise. Sci Rep 2020; 10:88. [PMID: 31919455 PMCID: PMC6952372 DOI: 10.1038/s41598-019-57081-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2019] [Accepted: 12/17/2019] [Indexed: 11/08/2022] Open
Abstract
We theoretically study the dynamical dephasing of a quantum two level system interacting with an environment which exhibits non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss the quantum dephasing dynamics of the system and the non-Markovian character exhibiting in the dynamical dephasing induced by non-Markovian random telegraph noise. We show that the dynamical dephasing of the quantum system does not always exhibit non-Markovian character which results from that the non-Markovian character in the dephasing dynamics depends both on the environmental non-Markovian character and the interaction between the system and environment. In addition, the dynamical dephasing of the quantum system can be modulated by the external modulation frequency of the environment. This result is significant to quantum information processing and helpful for further understanding non-Markovian dynamics of open quantum systems.
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Affiliation(s)
- Xiangji Cai
- School of Science, Shandong Jianzhu University, Jinan, 250101, China.
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Cai X, Zheng Y. Non-Markovian decoherence dynamics in nonequilibrium environments. J Chem Phys 2018; 149:094107. [PMID: 30195316 DOI: 10.1063/1.5039891] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We theoretically investigate the non-Markovian dynamical decoherence of a quantum system coupled to nonequilibrium environments with nonstationary statistical properties. We show the time evolution of the decoherence factor in real-imaginary space to study the environment-induced energy renormalization and backaction of coherence which are associated with the unitary and nonunitary parts of the quantum master equation, respectively. It is also shown that the nonequilibrium decoherence dynamics displays a transition between Markovian and non-Markovian and the transition boundary depends on the environmental parameters. The results are helpful for further understanding non-Markovian dynamics and coherence backaction on an open quantum system from environments.
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Affiliation(s)
- Xiangji Cai
- School of Physics, Shandong University, Jinan 250100, China
| | - Yujun Zheng
- School of Physics, Shandong University, Jinan 250100, China
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Szańkowski P, Ramon G, Krzywda J, Kwiatkowski D, Cywiński Ł. Environmental noise spectroscopy with qubits subjected to dynamical decoupling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:333001. [PMID: 28569239 DOI: 10.1088/1361-648x/aa7648] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.
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Affiliation(s)
- P Szańkowski
- Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland
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Allegrini P, Grigolini P, Palatella L, West BJ. Non-Poisson dichotomous noise: higher-order correlation functions and aging. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046118. [PMID: 15600471 DOI: 10.1103/physreve.70.046118] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2004] [Indexed: 05/24/2023]
Abstract
We study a two-state symmetric noise, with a given waiting time distribution psi (tau) , and focus our attention on the connection between the four-time and two-time correlation functions. The transition of psi (tau) from the exponential to the nonexponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.
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Affiliation(s)
- P Allegrini
- INFM, Unità di Como, Via Valleggio 11, 22100 Como, Italy
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Budini AA, Cáceres MO. Functional characterization of linear delay Langevin equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046104. [PMID: 15600457 DOI: 10.1103/physreve.70.046104] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2004] [Indexed: 05/24/2023]
Abstract
We present an exact functional characterization of linear delay Langevin equations driven by any noise structure defined through its characteristic functional. This method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise. General properties of the transient dissipative dynamics are analyzed. The corresponding interplay with a color Gaussian noise is presented. As a full application of our functional method we study a model for population growth with non-Gaussian fluctuations: the Gompertz model driven by multiplicative white shot noise.
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Affiliation(s)
- Adrián A Budini
- Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
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Aquino G, Bologna M, Grigolini P, West BJ. Aging and rejuvenation with fractional derivatives. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036105. [PMID: 15524585 DOI: 10.1103/physreve.70.036105] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2004] [Indexed: 05/24/2023]
Abstract
We discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index mu in the interval 2<mu<3 , yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, o , is given by o=3-mu . A brand new system is characterized by the degree o=mu-2 . If the system is prepared at time - t(a) <0 and the observation begins at time t=0 , we derive the following scenario. For times 0<t<< t(a) the system is satisfactorily described by the fractional derivative with o=3-mu . Upon time increase the system undergoes a rejuvenation process that in the time limit t>> t(a) yields o=mu-2 . The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.
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Affiliation(s)
- Gerardo Aquino
- Center for Nonlinear Science, University of North Texas, P. O. Box 311427, Denton, Texas 76203-1427, USA
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Bena I, Van Den Broeck C, Kawai R, Lindenberg K. Nonlinear response with dichotomous noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:045603. [PMID: 12443252 DOI: 10.1103/physreve.66.045603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2002] [Indexed: 05/24/2023]
Abstract
Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full analytic results for hypersensitive transport.
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Affiliation(s)
- I Bena
- Limburgs Universitair Centrum, B-3590 Diepenbeek, Belgium
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Yulmetyev R, Hanggi P, Gafarov F. Stochastic dynamics of time correlation in complex systems with discrete time. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:6178-6194. [PMID: 11101949 DOI: 10.1103/physreve.62.6178] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2000] [Revised: 07/03/2000] [Indexed: 05/23/2023]
Abstract
In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy S(i)(t) where i=0,1,2,3,ellipsis, as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,ellipsis). The set of functions S(i)(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,ellipsis) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function S(i)(t) for time correlation (i=0) and time memory (i=1,2,3,ellipsis). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG's shows convincing evidence for a non-Markovian phenomemena associated with a peculiarities in short- and long-range scaling. This method may be of use in distinguishing healthy from pathologic data sets based in differences in these non-Markovian properties.
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Affiliation(s)
- R Yulmetyev
- Department of Physics, University of Augsburg, Universitatsstrasse 1, D-86135 Augsburg, Germany and Department of Theoretical Physics, Kazan State Pedagogical University, Mezhlauk Street 1, 420021 Kazan, Russia
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Fuliński A. Transitions through fluctuating barrier: Role of asymmetry and memory. J Chem Phys 1997. [DOI: 10.1063/1.474797] [Citation(s) in RCA: 4] [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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Zygadlo R. Kinetics of a Verhulst-type system with nonlinearly coupled noise. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:5964-5968. [PMID: 9965812 DOI: 10.1103/physreve.54.5964] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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