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arXiv:1109.1239 · Physical Review A

Dynamics of interacting qubits coupled to a common bath: Non-Markovian quantum-state-diffusion approach

Xinyu Zhao, Jun Jing, Brittany Corn, Ting Yu

Published Sep 2, 2011• 71 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.84.032101

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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.
Non-Markovian dynamics of two interacting two-level qubits coupled to a bosonic bath was previously studied using the quantum-state-diffusion (QSD) equation, where a stochastic state is used to describe the system. In this study, we provide another perspective on this system by deriving the analytic form of the master equation, which describes the system with a reduced density matrix. Then, we validate the master equation by examining entanglement generation and state purity. In addition, with the master equation, we observe the effects from first-order noise and notice that a good asymptotic approximation to the master equation can be made by neglecting the first-order noise.
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.
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.
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.
The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schrödinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.
We investigate the non-Markovian quantum dynamics of a hybrid open system consisting of one qubit and one qutrit by employing a stochastic Schrödinger equation to generate diffusive quantum trajectories. We have established an exact quantum state diffusion (QSD) equation for the dissipative qubit-qutrit system coupled to a bosonic heat bath at zero temperature. As an important application, the non-Markovian QSD equation is employed to simulate the entanglement decay and generation measured by negativity. Finally, some steady-state properties of the hybrid system are also discussed.