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Chruściński D, Hesabi S, Lonigro D. On Markovianity and classicality in multilevel spin-boson models. Sci Rep 2023; 13:1518. [PMID: 36707631 PMCID: PMC9883298 DOI: 10.1038/s41598-023-28606-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2022] [Accepted: 01/20/2023] [Indexed: 01/28/2023] Open
Abstract
We provide a detailed discussion about the unitary and reduced evolution induced by family of Hamiltonian models describing a multilevel system, with a ground state and a possibly multilevel excited sector, coupled to a multimode boson field via a rotating-wave interaction. We prove explicitly that the system, in the limit in which the coupling is flat with respect to the boson frequencies, is Markovian under sharp measurements in arbitrary bases; we also find necessary and sufficient conditions under which the process is classical, i.e. its family of multitime joint probability distributions satisfies the Kolmogorov consistency condition, and may thus be equivalently obtained by a classical stochastic process.
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Affiliation(s)
- Dariusz Chruściński
- grid.5374.50000 0001 0943 6490Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland
| | - Samaneh Hesabi
- grid.5374.50000 0001 0943 6490Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Toruń, Poland
| | - Davide Lonigro
- grid.7644.10000 0001 0120 3326Dipartimento di Fisica and MECENAS, Università di Bari, 70126 Bari, Italy ,grid.470190.bINFN, Sezione di Bari, 70126 Bari, Italy
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2
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Lin MC, Lo PY, Nori F, Chen HB. Precession-induced nonclassicality of the free induction decay of NV centers by a dynamical polarized nuclear spin bath. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:505701. [PMID: 36261040 DOI: 10.1088/1361-648x/ac9bbe] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2022] [Accepted: 10/19/2022] [Indexed: 06/16/2023]
Abstract
The ongoing exploration of the ambiguous boundary between the quantum and the classical worlds has spurred substantial developments in quantum science and technology. Recently, the nonclassicality of dynamical processes has been proposed from a quantum-information-theoretic perspective, in terms of witnessing nonclassical correlations with Hamiltonian ensemble simulations. To acquire insights into the quantum-dynamical mechanism of the process nonclassicality, here we propose to investigate the nonclassicality of the electron spin free-induction-decay process associated with an NV-center. By controlling the nuclear spin precession dynamics via an external magnetic field and nuclear spin polarization, it is possible to manipulate the dynamical behavior of the electron spin, showing a transition between classicality and nonclassicality. We propose an explanation of the classicality-nonclassicality transition in terms of the nuclear spin precession axis orientation and dynamics. We have also performed a series of numerical simulations supporting our findings. Consequently, we can attribute the nonclassical trait of the electron spin dynamics to the behavior of nuclear spin precession dynamics.
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Affiliation(s)
- Mu-Che Lin
- Department of Engineering Science, National Cheng Kung University, Tainan 701401, Taiwan
| | - Ping-Yuan Lo
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300093, Taiwan
| | - Franco Nori
- Quantum Computing Center, and Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wakoshi, Saitama 351-0198, Japan
- Physics Department, University of Michigan, Ann Arbor, MI 48109-1040, United States of America
| | - Hong-Bin Chen
- Department of Engineering Science, National Cheng Kung University, Tainan 701401, Taiwan
- Center for Quantum Frontiers of Research & Technology, NCKU, Tainan 701401, Taiwan
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3
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Anderson MC, Schile AJ, Limmer DT. Nonadiabatic transition paths from quantum jump trajectories. J Chem Phys 2022; 157:164105. [DOI: 10.1063/5.0102891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. We detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.
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Affiliation(s)
- Michelle C. Anderson
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Addison J. Schile
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T. Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Montes G, Biswas S, Gorin T. From classical to quantum stochastic processes. Phys Rev E 2022; 105:064130. [PMID: 35854561 DOI: 10.1103/physreve.105.064130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 06/06/2022] [Indexed: 06/15/2023]
Abstract
In this paper, we construct quantum analogs starting from classical stochastic processes, by replacing random "which path" decisions with superpositions of all paths. This procedure typically leads to nonunitary quantum evolution, where coherences are continuously generated and destroyed. In spite of their transient nature, these coherences can change the scaling behavior of classical observables. Using the zero temperature Glauber dynamics in a linear Ising spin chain, we find quantum analogs with different domain growth exponents. In some cases, this exponent is even smaller than for the original classical process, which means that coherence can play an important role to speed up the relaxation process.
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Affiliation(s)
- Gustavo Montes
- Departamento de Física, CUCEI, Universidad de Guadalajara, Guadalajara, Jalísco, C.P.-44430, Mexico
- Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Instituto de Física, 72570 Puebla, Mexico
- Quantum Biology Laboratory, Howard University, Washington, DC 20059, USA
| | - Soham Biswas
- Departamento de Física, CUCEI, Universidad de Guadalajara, Guadalajara, Jalísco, C.P.-44430, Mexico
| | - Thomas Gorin
- Departamento de Física, CUCEI, Universidad de Guadalajara, Guadalajara, Jalísco, C.P.-44430, Mexico
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5
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Effects of symmetry breaking of the structurally-disordered Hamiltonian ensembles on the anisotropic decoherence of qubits. Sci Rep 2022; 12:2869. [PMID: 35190613 PMCID: PMC8861020 DOI: 10.1038/s41598-022-06891-4] [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: 12/17/2021] [Accepted: 02/08/2022] [Indexed: 11/09/2022] Open
Abstract
It is commonly known that the dephasing in open quantum systems is due to the establishment of bipartite correlations with ambient environments, which are typically difficult to be fully characterized. Recently, a new approach of average over disordered Hamiltonian ensemble is developed and shown to be capable of describing the nonclassicality of incoherent dynamics based on inferring the nonclassical nature of the correlations. Here we further extend the approach of Hamiltonian ensemble in the canonical form to the realm of structural disorder. Under the variable separation of the probability distribution within the Hamiltonian ensemble, the geometrical structure is easily visualized and can be characterized according to the degree of symmetry. We demonstrate four degrees and investigate the effects of different types of symmetry breaking on the incoherent dynamics. We show that these effects are easily understood from the emergences of additional terms in the master equations, leading to rather general master equations and, consequently, going beyond the previous frameworks of pure dephasing or isotropic depolarization.
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Seif A, Wang YX, Clerk AA. Distinguishing between Quantum and Classical Markovian Dephasing Dissipation. PHYSICAL REVIEW LETTERS 2022; 128:070402. [PMID: 35244435 DOI: 10.1103/physrevlett.128.070402] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Revised: 12/09/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
Understanding whether dissipation in an open quantum system is truly quantum is a question of both fundamental and practical interest. We consider n qubits subject to correlated Markovian dephasing and present a sufficient condition for when bath-induced dissipation can generate system entanglement and hence must be considered quantum. Surprisingly, we find that the presence or absence of time-reversal symmetry plays a crucial role: broken time-reversal symmetry is required for dissipative entanglement generation. Further, simply having nonzero bath susceptibilities is not enough for the dissipation to be quantum. We also present an explicit experimental protocol for identifying truly quantum dephasing dissipation and lay the groundwork for studying more complex dissipative systems and finding optimal noise mitigating strategies.
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Affiliation(s)
- Alireza Seif
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Yu-Xin Wang
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Aashish A Clerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
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Canonical Hamiltonian ensemble representation of dephasing dynamics and the impact of thermal fluctuations on quantum-to-classical transition. Sci Rep 2021; 11:10046. [PMID: 33976361 PMCID: PMC8113319 DOI: 10.1038/s41598-021-89400-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 04/26/2021] [Indexed: 12/02/2022] Open
Abstract
An important mathematical tool for studying open quantum system theory, which studies the dynamics of a reduced system, is the completely positive and trace-preserving dynamical linear map parameterized by a special parameter-time. Counter-intuitively, akin to the Fourier transform of a signal in time-sequence to its frequency distribution, the time evolution of a reduced system can also be studied in the frequency domain. A recent proposed idea which studies the representation of dynamical processes in the frequency domain, referred to as canonical Hamiltonian ensemble representation (CHER), proved its capability of characterizing the noncalssical traits of the dynamics. Here we elaborate in detail the theoretical foundation within a unified framework and demonstrate several examples for further studies of its properties. In particular, we find that the thermal fluctuations are clearly manifested in the manner of broadening CHER, and consequently rendering the CHER less nonclassical. We also point out the discrepancy between the notions of nonclassicality and non-Markovianity, show multiple CHERs beyond pure dephasing, and, finally, to support the practical viability, propose an experimental realization based upon the free induction decay measurement of nitrogen-vacancy center in diamond.
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Faint trace of a particle in a noisy Vaidman three-path interferometer. Sci Rep 2021; 11:1123. [PMID: 33441893 PMCID: PMC7806841 DOI: 10.1038/s41598-020-80806-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 12/28/2020] [Indexed: 12/05/2022] Open
Abstract
We study weak traces of particle passing Vaidman’s nested Mach–Zehnder interferometer. We investigate an effect of decoherence caused by an environment coupled to internal degree of freedom (a spin) of a travelling particle. We consider two models: pure decoherence leading to exact results and weak coupling Davies approximation allowing to include dissipative effects. We show that potentially anomalous discontinuity of particle paths survives an effect of decoherence unless it affects internal part of the nested interferometer.
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Abstract
We analyze the conditions under which the dynamics of a quantum system open to a given environment can be simulated with an external noisy field that is a surrogate for the environmental degrees of freedom. We show that such a field is either a subjective or an objective surrogate; the former is capable of simulating the dynamics only for the specific system–environment arrangement, while the latter is an universal simulator for any system interacting with the given environment. Consequently, whether the objective surrogate field exists and what are its properties is determined exclusively by the environment. Thus, we are able to formulate the sufficient criterion for the environment to facilitate its surrogate, and we identify a number of environment types that satisfy it. Finally, we discuss in what sense the objective surrogate field representation can be considered classical and we explain its relation to the formation of system–environment entanglement, and the back-action exerted by the system onto environment.
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