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arXiv:1807.01721 · Physical Review A

Noise-induced non-Markovianity

Arzu Kurt, Resul Eryiğit

Published Oct 23, 2018• 8 citations
arXivHTMLPDF

Abstract

We have studied the non-Markovianity of a dichotomously driven spin-boson model in the strong-coupling regime in both memory kernel and time convolutionless master-equation formulations. A strong correlation between the decay time of the environmental correlation function and the nonzero non-Markovianity is found in the absence of the external noise. Stochastic driving is shown to create strong non-Markovianity when the dynamics of the system without driving is Markovian. Also, exact analytical expressions for the trace distance distinguishability and the non-Markovianity were obtained for the certain range of the parameters that describe the system and its environment.

DOI
10.1103/physreva.98.042125

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We have studied the non-Markovianity of a dichotomously driven spin-boson model in the strong-coupling regime in both memory kernel and time convolutionless master-equation formulations. A strong correlation between the decay time of the environmental correlation function and the nonzero non-Markovianity is found in the absence of the external noise. Stochastic driving is shown to create strong non-Markovianity when the dynamics of the system without driving is Markovian. Also, exact analytical expressions for the trace distance distinguishability and the non-Markovianity were obtained for the certain range of the parameters that describe the system and its environment.
We investigate signatures of non-Markovianity in the dynamics of a periodically driven qubit coupled to a dissipative bosonic environment. We propagate the dynamics of the reduced density matrix of the qubit by integrating the numerically exact hierarchical equations of motion. Non-Markovian features are quantified by comparing on an equal footing the predictions from diverse and complementary approaches to quantum dissipation. In particular, we analyze the distinguishability of quantum states, the decay of the volume accessible to the qubit on the Hilbert space, the negativity of the canonical rates in the generalized Lindblad equation, and the relaxation of the memory kernels in the Nakajima-Zwanzig generalized quantum master equation. We study the effects of controlled driving on the coherent dynamics of the system. We show that a suitable external field can offset the ergodic relaxation of time-correlation functions, increase distinguishability over time, and strengthen non-Markovian effects witnessed by the canonical dissipation channels. We furthermore observe the phenomenon of eternal non-Markovianity for sufficiently small system-bath coupling and we discuss how this can be enhanced by modulating the frequency of the external drive. This work provides a broad theoretical analysis of quantum dissipation in the framework of open quantum dynamics and quantum information.
Employing a recently proposed measure for quantum non-Markovianity, we carry out a systematic study of the size of memory effects in the spin-boson model for a large region of temperature and frequency cutoff parameters. The dynamics of the open system is described utilizing a second-order time-convolutionless master equation without the Markov or rotating wave approximations. While the dynamics is found to be strongly non-Markovian for low temperatures and cutoffs, in general, we observe a special regime favoring Markovian behavior. This effect is explained as resulting from a resonance between the system's transition frequency and the frequencies of the dominant environmental modes. We further demonstrate that the corresponding Redfield equation is capable of reproducing the characteristic features of the non-Markovian quantum behavior of the model.
The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have investigated the non-Markovianity of the dynamics of a two-state system driven by continuous time random walk-type noise, which can be Markovian or non-Markovian depending on its residence time distribution parameters. Exact analytical expressions for the distinguishability as well as the trace distance and entropy-based non-Markovianity measures are obtained and used to investigate the interplay between the non-Markovianity of the noise and that of dynamics. Our results show that, in many cases, the dynamics are also non-Markovian when the noise is non-Markovian. However, it is possible for Markovian noise to cause non-Markovian dynamics and for non-Markovian noise to cause Markovian dynamics but only for certain parameter values.
We derive a time-convolutionless master equation for the spin-boson model in the weak coupling limit. The temporarily negative decay rates in the master equation indicate short time memory effects in the dynamics which is explicitly revealed when the dynamics is studied using the non-Markovian jump description. The approach gives new insight into the memory effects influencing the spin dynamics and demonstrates, how for the spin-boson model the the co-operative action of different channels complicates the detection of memory effects in the dynamics.
Abstract Non-Markovian dynamics is central to quantum information processing, as memory effects strongly influence coherence preservation, metrology, and communication. In this work, we investigate the role of stochastic system–bath couplings in shaping non-Markovian behavior of open quantum systems, using the central spin model within a time-convolutionless master equation framework. We show that the character of the reduced dynamics depends jointly on the intrinsic memory of the environment and on the structure of the system–environment interaction. In certain regimes, the dynamics simplify to pure dephasing, while in general both amplitude damping and dephasing contribute to the evolution. By employing two complementary measures: the Quantum Fisher Information (QFI) flow and the Breuer–Laine–Piilo (BLP) measure, we demonstrate that QFI flow may fail to witness memory effects in weak-coupling and near-resonant regimes, whereas the BLP measure still detects information backflow. Furthermore, external modulation of the interaction kernel produces qualitatively richer behavior, including irregular and frequency-dependent revivals of non-Markovianity. These results clarify the physical origin of memory effects, highlight the limitations of single-witness approaches, and suggest that stochasticity and modulation can be harnessed to engineer robust, noise-resilient quantum technologies.
Using a recently proposed measure for divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a driven spin-SSS system weakly coupled to a bosonic bath. The complete tomographic knowledge about the dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. The derived equation can be applied to a wide range of spin-boson models with the Hermitian or non-Hermitian coupling operator in the system-environment interaction Hamiltonian. Besides the influence of the environmental spectral densities, the tunneling energy of the system Hamiltonian can affect the measure of quantum non-Markovianity. It is found that the non-Markovian feature of a dynamical map of a high-dimension spin system is noticeable in contrast to that of a low-dimension spin system.