Entanglement and Its Dynamics with Atomic Spontaneous Decay

The atomic decay for a two-level atom interacting with a single mode of electromagnetic tield is considered. For a chosen initial state, the exact solution of the master equation is found. Therefore, effect of the atomic damping on entanglement （purity loss）, degree of entanglement by the negativity, mutual information and atomic coherence through the master equation are studied.     

Non-Markovian master equation for a system of Fermions interacting with an electromagnetic field

For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad’s form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell-Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots.     

Non-Markovian dynamics of a qubit in a reservoir: different solutions of non-Markovian master equation

We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.     

Solving non-Markovian open quantum systems with multi-channel reservoir coupling

We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein–Uhlenbeck reservoir correlations numerically.     

Non-Markovian relaxation of a three-level system: quantum trajectory approach

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 Schr?dinger 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.     

Exact decoherence dynamics of a single-mode optical field

We apply the influence-functional method of Feynman and Vernon to the study of a single-mode optical field that interacts with an environment at zero temperature. Using the coherent-state formalism of the path integral, we derive a generalized master equation for the single-mode optical field. Our analysis explicitly shows how non-Markovian effects manifest in the exact decoherence dynamics for different environmental correlation time scales. Remarkably, when these are equal to or greater than the time scale for significant change in the system, the interplay between the backaction-induced coherent oscillation and the dissipative effect of the environment causes the non-Markovian effect to have a significant impact not only on the short-time behavior but also on the long-time steady-state behavior of the system.     

The population and decay evolution of a qubit under the time-convolutionless master equation

We consider the population and decay of a qubit under the electromagnetic environment. Employing the time-convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper.     

Non-equilibrium effects upon the non-Markovian Caldeira–Leggett quantum master equation

We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker–Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira–Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.     

Enhanced squeezing and entanglement in a non-degenerate three-level cascade laser with injected squeezed light

We consider a non-degenerate three-level cascade laser coupled to a two-mode squeezed vacuum reservoir via the lossy single-port mirror. Applying the pertinent master equation, we analyze the effects of the injected squeezed light on the quadrature squeezing, entanglement and normalized intensity difference fluctuations. We show that the injected squeezed light considerably enhances the degree of squeezing and entanglement in the two-mode light for certain initial conditions. Moreover, the injected squeezed light increases the mean photon number where the squeezing and entanglement is significant. We also show that the presence of the injected squeezed light greatly reduces the noise in the intensity difference.     

Markovian and non-Markovian solution of the generalized master equation for dynamics of particle transfer in a symmetric double-well potential

Dynamics of particle transfer in a symmetric double-well potential has been investigated. In restriction to two-level system, the convolution form of generalized master equation with retention of off-diagonal matrix elements has been solved on non-Markovian level as well in Markov approximation. It has been shown that subsystem dynamics crucially depends on interplay of three variables, correlation time of an environment, dephasing time and coherent transfer time. The character of dynamics then varies from damped oscillations through exponential decay and incoherent relaxation. It has been shown that on non-Markovian level, under some circumstances, the particle transfer is governed by the dynamics of slow environment.     

Master equations with memory for systems driven by classical noise

A non-Markovian master equation is obtained for a two level atom driven by a phase noisy laser. The derivation is based on obtaining an equation for the density operator of the system averaged over the previous histories of the external noise. Averaging over the current value of the noise variable by means of the Zwanzig-Nakajima projection operator technique leads to a master equation with memory and a local-in-time master equation. The solutions to the resultant non-Markovian master equation, the structural properties of the equation, and the amenability of the equation to unravelling by the quantum trajectory method are all investigated.     

Decoherence in atom–field interactions: A treatment using superoperator techniques

Decoherence is a subject of great importance in quantum mechanics, particularly in the fields of quantum optics, quantum information processing and quantum computing. Quantum computation relies heavily in the unitary character of each step carried out by a quantum computational device and this unitarity is affected by decoherence. An extensive study of master equations is therefore needed for a better understanding on how quantum information is processed when a system interacts with its environment. Master equations are usually studied by using Fokker–Planck and Langevin equations and not much attention has been given to the use of superoperator techniques. In this report we study in detail several approaches that lead to decoherence, for instance a variation of the Schrödinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. For the study of the dissipative interaction we use a correspondence principle approach. We solve the master equations for different physical systems, namely, Kerr and parametric down conversion. In the case of light-matter interaction we show that although dissipation destroys the quantumness of the field, information of the initial field may be obtained via the reconstruction of quasiprobability distribution functions.     

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number(n)-resolved master equation(ME) approach under the self-consistent Born approximation(SCBA) for quantum transport through mesoscopic systems.The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations.The proposed n-SCBA-ME goes beyond the scope of the BornMarkov master equation,being applicable to transport under small bias voltage,in non-Markovian regime and with strong Coulomb correlations.For steady state,it can recover not only the exact result of noninteracting transport under arbitrary voltages,but also the challenging nonequilibrium Kondo efect.Moreover,the n-SCBA-ME approach is efcient for the study of shot noise.We demonstrate the application by a couple of representative examples,including particularly the nonequilibrium Kondo system.     

Measurement master equation

We derive a master equation describing the evolution of a quantum system subjected to a sequence of observations. These measurements occur randomly at a given rate and can be of a very general form. As an example, we analyse the effects of these measurements on the evolution of a two-level atom driven by an electromagnetic field. For the associated quantum trajectories we find Rabi oscillations, Zeno-effect type behaviour and random telegraph evolution spawned by mini quantum jumps as we change the rates and strengths of measurement.     

Entanglement dynamics of two interacting qubits under the influence of local dissipation

We investigate the dynamics of entanglement given by the concurrence of a two-qubit system in the non-Markovian setting. A quantum master equation is derived, which is solved in the eigenbasis of the system Hamiltonian for X-type initial states. A closed formula for time evolution of concurrence is presented for a pure state. It is shown that under the influence of dissipation non-zero entanglement is created in unentangled two-qubit states which decay in the same way as pure entangled states. We also show that under real circumstances, the decay rate of concurrence is strongly modified by the non-Markovianity of the evolution.     

Non-Markovian and Markovian Dynamics of a V-type Three-Level Atom

The reduced dynamics of a V-type three-level atom in a structure reservoir is presented,which has the exact solution in certain special condition.The Markovian and non-Markovian master equations for this composite system are solved and compared with the exact solution.The solving approach can be directly generalized to the solution of a V-type multilevel system dynamics interacting with a reservoir.The results further testify that these two kinds of master equations are exploited in different coupling regime,providing guidance for further application of these variants master equations to solve multilevel system dynamics without the exact solution.     

Population relaxation effects on entanglement dynamics of the two-qubit spin chains

By analytically solving the master equation, we examine entanglement dynamics of the two-qubit spin system coupled via the XY interaction and in the presence of population relaxation. We found that the entanglement dynamical behaviors are very sensitive to different initialized states. Particularly, for initial states ?=(|01〉〈01|+|10〉〈10|)/2 and ?=(|00〉〈00|+|11〉〈11|)/2, a combination of the XY coupling with the population relaxation can even be used to enhance the entanglement. Moreover, we show that among different initially separable states, ?=|01〉〈01| and ?=|10〉〈10| are more robust in generating pairwise entanglement.