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arXiv:1105.1358

Non-Markovian Diffusive Unravellings of Entanglement

Brittany Corn, Jun Jing, Ting Yu

Published May 6, 2011• 0 citations
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Abstract

The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the two-qubit dissipative and dephasing models. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the system state space.

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The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the two-qubit dissipative and dephasing models. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the system state space.
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Non-Markovian dynamics is studied for two interacting qubits strongly coupled to a dissipative bosonic environment. We derive a non-Markovian quantum-state-diffusion (QSD) equation for the coupled two-qubit system without any approximations, and in particular, without the Markov approximation. As an application and illustration of our derived time-local QSD equation, we investigate the temporal behavior of quantum coherence dynamics. In particular, we find a strongly non-Markovian regime where entanglement generation is significantly modulated by the environmental memory. Additionally, we study residual entanglement in the steady state by analyzing the steady-state solution of the QSD equation. Finally, we discuss an approximate QSD equation.
A long-standing open problem in the non-Markovian quantum state diffusion (QSD) approach to open quantum systems is to establish the non-Markovian QSD equations for multiple-qubit systems. In this paper, we settle this important question by explicitly constructing a set of exact time-local QSD equations for NNN-qubit systems. Our exact time-local (convolutionless) QSD equations have paved the way towards simulating quantum dynamics of many-body open systems interacting with a common bosonic environment. The applicability of this multiple-qubit stochastic equation is exemplified by numerically solving several quantum open many-body systems concerning quantum coherence dynamics and dynamical control.
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We present a perturbation theory for non-Markovian quantum-state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Phys. Rev. A 58, 1699 (1998)]. We establish a systematic expansion in the ratio between the environmental correlation time and the typical system time scale. The leading order recovers the Markov theory, so here we concentrate on the next-order correction corresponding to first-order non-Markovian master equations. These perturbative equations greatly simplify the general non-Markovian QSD approach, and allow for efficient numerical simulations beyond the Markov approximation. Furthermore, we show that each perturbative scheme for QSD naturally gives rise to a perturbative scheme for the master equation which we study in some detail. Analytical and numerical examples are presented, including the quantum Brownian motion model.
We provide a thorough analysis of the entanglement dynamics of an interacting two-qubit system in the non-Markovian regime. In such a regime, the time scale on which the reservoir degrees of freedom evolve is either of the same order of magnitude or less than that on which the system evolves. We used an exact numerical method; the Quasi-Adiabatic Path Integral (QUAPI) technique, to describe the corresponding qubit dissipative dynamics in such a non-Markovian regime. We computed the time evolution of the density operator for the quibits, from which we quantified the coherences and population dynamics, as well as the qubit-bath coupling effects. Using negativity as a metric, we calculated the dynamics of non-local quantum correlations (entanglement), and indentified a non-Markovian quantum phenomena in terms of early stage disentanglement, and the collapse and revival of entanglement.