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Communications in Theoretical Physics

Non-Markovianity and Indivisible Quantum dynamics of a Apin- S System

Xiang Hao, Xuefen Xu, Shiqun Zhu

Published Sep 1, 2013• 1 citation
Publisher

Abstract

Using a measure for the divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a spin-S system, which is in an external field and weakly coupled to a bosonic bath with a certain temperature. The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. Besides the influence of the environmental spectral density function, the external field and low temperatures can affect the quantum non-Markovianity. It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.

DOI
10.1088/0253-6102/60/3/09

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Using a measure for the divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a spin-S system, which is in an external field and weakly coupled to a bosonic bath with a certain temperature. The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. Besides the influence of the environmental spectral density function, the external field and low temperatures can affect the quantum non-Markovianity. It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.
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.
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.
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 examine different nonlinear open quantum systems and calculate the non-Markovianity based on the distinguishability between two density matrices. We show that for a single spin (qubit) coupled to a bosonic field the non-Markovianity depends on the spectral density function and can take on any number N with 0 ≤ N ≤ 1, meaning the dynamics can be Markovian or highly non-Markovian. For the main result we consider a system of Ntot identical spins coupled to an environment in the mean-field way. Each spin is coupled to a local and the common reservoir. There are only indirect interactions between the spins through the common reservoir. In limit Ntot → 1 the subsystem consisting of a fixed set of n particles reduces to a factorized state in which each factor is a single spin evolving according to a nonlinear Hartree-Lindblad equation which is exactly solvable. For non-stationary initial spin states the non-Markovianity diverges. In this instance we can never approximate the dynamics of the quantum system by a Markovian master equation and this implies that in the mean field models, memory effects are significant.
The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the 'spin bath' model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.
We study the dynamics of a dressed qubit implemented by a spinless fermion hopping between two lattice sites with each site strongly coupled to a bath of phonons. We employ Lang-Firsov transformation to make the problem tractable perturbatively. Applying time-convolutionless master equation within the polaron frame, we investigate decoherence dynamics of the dressed qubit within the singlet-triplet basis of the system for a wide range of bath spectral densities. It is shown that the coherence persists for longer time scales for large coupling values and shows non-monotonic behaviour reflecting the presence of non-Markovianity in the dynamics. Non-Markovianity, characterized by coherence revivals and non-monotonic decay patterns, emerges distinctly depending on the bath spectrum and coupling strengths. Systems coupled to sub-Ohmic baths, whether both or in combination with another type, display pronounced memory effects at relatively small values of couplings. In contrast, combinations involving Ohmic and super-Ohmic baths exhibit noticeable non-Markovianity only at higher couplings.