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Journal of Physics B Atomic Molecular and Optical Physics

Exact entanglement dynamics mediated by leaky optical cavities

Yusui Chen, Quanzhen Ding, Wufu Shi, Jing Jun, Ting Yu

Published Jan 27, 2020• 7 citations
Publisher

Abstract

Abstract We present a quantum-state-diffusion equation to characterize the dynamics of a generic atomic system due to the coupling to a leaky cavity mode. As quantum resources, the population, the coherence and even the entanglement of the system would gradually leak out of the cavity. The effect from the leakage of the cavity-mode to the uncontrollable degrees of freedom, e.g. environment, is however not always negative to particular applications of these quantum resources. We investigate the competition between these two mechanisms in the framework of the non-Markovian open-quantum-system dynamics, where the leaky mode serves as a general two-layer bosonic environment. Numerical calculations based on our non-perturbative approach reveal a generation of quantum entanglement in the qubit system due to the coupling to a resonant leaky cavity.

DOI
10.1088/1361-6455/ab707c

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Abstract We present a quantum-state-diffusion equation to characterize the dynamics of a generic atomic system due to the coupling to a leaky cavity mode. As quantum resources, the population, the coherence and even the entanglement of the system would gradually leak out of the cavity. The effect from the leakage of the cavity-mode to the uncontrollable degrees of freedom, e.g. environment, is however not always negative to particular applications of these quantum resources. We investigate the competition between these two mechanisms in the framework of the non-Markovian open-quantum-system dynamics, where the leaky mode serves as a general two-layer bosonic environment. Numerical calculations based on our non-perturbative approach reveal a generation of quantum entanglement in the qubit system due to the coupling to a resonant leaky cavity.
We present a quantum-state-diffusion equation to characterize the dynamics of a generic atomic system coupled to a leaky cavity mode. As quantum resources, the population, the coherence and even the entanglement of the system would gradually leak out of the cavity. The effect from the leakage of the cavity-mode to the uncontrollable degree of freedom, e.g., environment, is however not always negative to particular targets. A well-established scenario is that a photon counter attached to the cavity would absorb and then record the leaking photon. As a medium between the system and the photon counter, a strong coupling between system and cavity is necessary to enhance the measurement efficiency. While we find it also reduce the reading efficiency of the photon counter at the same time as fewer photons leak out of the cavity. We investigate the competition between these two mechanisms in the framework of non-Markovian open-quantum-system dynamics, where the photon counter serves as a general bosonic environment. Our results provide an optimized parameter space for system entanglement preservation and generation.
Abstract All realistic quantum systems will interact with their environments. This fact presents challenges to the implementation of quantum systems for practical systems. One of the most important quantum resources is the implementation of entanglement. In this paper, we investigate the interplay between the effects of noisy environments and the dynamics of entanglement. The open quantum system model that will be used is cavity quantum electrodynamics (CQED) with three-qubit interacting independently with a variation of environmental model. We use master equation to describe the dynamics of the open quantum system and a lower bound concurrence (CLBC ) to measure the entanglement of tripartite qubit. We derive the exact dynamics of each model and use CLBC method proposed by Li et.al to visualize entanglement dynamics. By adjusting the environmental parameters, we also found revivals and dark-periods of entanglement which are unique to non-Markovian processes.
In this review we discuss recent progress in the theory of open quantum systems based on non-MarkovianNon-Markovian quantum state diffusionQuantum state diffusion equation and master equationsMaster equation. In particular, we show that an exact master equation for an open quantum system consisting of a few qubits can be explicitly constructed by using the corresponding non-Markovian quantum state diffusion equation. The exact master equation arises naturally from the quantum decoherence dynamics of qubit systems collectively interacting with a colored noise. We illustrate our general theoretical formalism by the explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This exact qubit master equation accurately characterizes the time evolution of the qubit system in various parameter domains, and paves the way for investigation of the memory effect of an open quantum system in a non-Markovian regime without any approximation.
Using an exact approach, we study the dynamics of entanglement between two qubits coupled to independent reservoirs and between the two, initially disentangled, reservoirs. We also describe the transfer of bipartite entanglement from the two qubits to their respective reservoirs focussing on the case of two atoms inside two different leaky cavities with a specific attention to the role of the detuning. We present a scheme to prepare the cavity fields in a maximally entangled state, without direct interaction between the cavities, by exploiting the initial qubits entanglement. We discuss a deterministic protocol, working in the presence of cavity losses, for the generation of a W-state of one qubit and two cavity fields and we describe a probabilistic scheme to entangle one of the atoms with the reservoir (cavity field) of the other atom.
We apply the stochastic Schr\"odinger equation approach to study the non-Markovian dynamics of quantum systems coupled to a squeezed environment. We derive the non-Markovian quantum-state-diffusion equation using coherent-state unraveling and the associated zeroth-order master equation for general models in a microscopic quantum context. Focused on a dissipative optical cavity coupled with a squeezed vacuum, the numerical simulations demonstrate the time evolution of photon numbers in an optical cavity. We observe that the long-time limits of the non-Markovian dynamics are significantly different from those of the Markovian dynamics for various memory factors and squeezing factors. Additionally, non-Markovian dynamics exhibit a distinct pattern of behavior when parameters change. Our work provides a method to study the impact of multiple parameters on the non-Markovian dynamics and long-time limits in a joint manner. The method can be further extended to squeezed finite-temperature environments.
Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.