non-Markovian Reservoir Research Articles

Non-Markovian dynamics of two non-coupled qubits interacting with two separate reservoirs with different spectral densities

The dynamics of two non-coupled qubits independently interacting with their reservoirs is solved by the time convolutionless projection operator method. We study two-qubit quantum correlation dynamics for two different types of spectral densities, which are a Lorentzian distribution and an Ohmic spectral density with a Lorentzian—Drude cutoff function. For two qubits initially prepared in the initial Bell state, quantum discord can keep longer time and reach larger values in non-Markovian reservoirs for the first spectral distribution or by reducing the cutoff frequency for the second case. For the initial Bell-like state, the dynamic behaviors of quantum discord and entanglement are compared. The results show that a long time of quantum correlation can be obtained by adjusting some parameters in experiment and further confirm that the discord can capture quantum correlation in addition to entanglement.

Quantum correlation dynamics of three non-coupled two-level atoms in different reservoirs

Time evolution dynamics of three non-coupled two-level atoms independently interacting with their reservoirs is solved exactly by considering a damping Lorentzian spectral density. For three atoms initially prepared in Greenberger—Horne—Zeilinger-type state, quantum correlation dynamics in a Markovian reservoir is compared with that in a non-Markovian reservoir. By increasing detuning quantity in the non-Markovian reservoir, three-atom correlation dynamics measured by negative eigenvalue presents a trapping phenomenon which provides long-time quantum entanglement. Then we compare the correlation dynamics of three atoms with that of two atoms, measured by quantum entanglement and quantum discord for an initial robuster-entangled type state. The result further confirms that quantum discord is indeed different from quantum entanglement in identifying quantum correlation of many bodies.

High Degree Entanglement Generation of Two Atoms in a Common Non-Markovian Reservoir with Dipole-Dipole Interaction

A system of two interacting qubits off-resonantly coupled to a common non-Markovian reservoir at zero temperature is analyzed. Comparing with the results in Markovian case, we find that much higher values of entanglement can be obtained for an initially factorized state of the two-qubit system. The maximal value of the entanglement increases as the strength of dipole-dipole interaction and detuning grow. Moreover, the entanglement induced by non-Markovian reservoir is more robust against the asymmetrical couplings between the two qubits and the reservoir.

Entanglement backflow under the composite effect of two non-Markovian reservoirs

The entanglement backflow of two qubits coupled to two independent reservoirs is investigated. It is found that under the collective effects of the two independent reservoirs, the entanglement backflow of the qubits does not always increase with the increase of the non-Markovianity of one of the reservoirs but demonstrates an intricate behavior. Interestingly, the action of one reservoir can affect the other reservoirʼs contribution to the entanglement backflow even when the two reservoirs are independent.

Quantum teleportation in a dissipative environment

We investigate quantum teleportation of a single-qubit state for the situation in which both qubits of the entangled channel are subjected to local structured reservoirs. We consider the effect of entanglement sudden death (ESD) of the channel on the average fidelity of the teleportation. It is shown the appearance of ESD leads to an abrupt variation of the fidelity of quantum teleportation. In addition, we show the fidelity exhibits oscillations in the non-Markovian reservoir due to the memory effect of the reservoir.

Decoherence suppression of open quantum systems through a strong coupling to non-Markovian reservoirs

In this paper, we provide a mechanism of decoherence suppression for open quantum systems in general, and that for "Schrodinger cat-like" state in particular, through the strong couplings to non-Markovian reservoirs. Different from the usual strategies of suppressing decoherence by decoupling the system from the environment in the literatures, here the decoherence suppression employs the strong back-reaction from non-Markovian reservoirs. The mechanism relies on the existence of the singularities (bound states) of the nonequilibrium retarded Green function which completely determines the dissipation and decoherence dynamics of open systems. As an application, we examine the decoherence dynamics of a photonic crystal nanocavity that is coupled to a waveguide. The strong non-Markovian suppression of decoherence for the optical cat state is attained.

Linear entropy in quantum phase space

We calculate the quantum Renyi entropy in a phase space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner product divergences. The preferred method is to use generalized Gaussian phase space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

Quantum Discord Dynamics in Two Different Non-Markovian Reservoirs

The quantum discord dynamics of two non-coupled two-level atoms independently interacting with their reservoir is studied under two kinds of non-Markovian conditions, namely, an off-resonant case with atomic transition frequency and a photonic band gap. In the first case, the phenomenon of the quantum discord loss and the oscillatory behavior of the quantum discord can occur by changing the detuning quantity and reducing the spectral coupling width for any initial Bell state. Under the second condition, the trapping phenomenon of the quantum discord can be presented by adjusting the width of gap, that is, the quantum discord of two atoms keep a nonzero constant for a long time.

High entanglement generation and high fidelity quantum state transfer in a non-Markovian environment

This paper analyses a system of two independent qubits off-resonantly coupled to a common non-Markovian reservoir at zero temperature. Compared with the results in Markovian reservoirs, we find that much higher values of entanglement can be obtained for an initially factorized state of the two-qubit system. The maximal value of the entanglement increases as the detuning grows. Moreover, the entanglement induced by non-Markovian environments is more robust against the asymmetrical couplings between the two qubits and the reservoir. Based on this system, we also show that quantum state transfer can be implemented for arbitrary input states with high fidelity in the non-Markovian regime rather than the Markovian case in which only some particular input states can be successfully transferred.

Protecting the squeezing of a two-level system by detuning in non-Markovian environments

Squeezing of a two-level atom off-resonantly coupled to a non-Markovian reservoir is investigated. We compared two different definitions of squeezing that are based on the Heisenberg uncertainty relation and the entropy uncertainty relation and found that information entropy squeezing is more precise than variance squeezing as a measure of squeezing. Then we utilized entropy squeezing to examine the influences of the non-Markovian effect and detuning on the atomic squeezing. It is interesting to note that atomic squeezing can be protected for a long time when both the non-Markovian effect and detuning are present simultaneously. The physical mechanism is that the decay rate is suppressed much more by detuning in the non-Markovian regime than in the Markovian case.

FROZEN DISCORD IN NON-MARKOVIAN DEPHASING CHANNELS

We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.

Non-Markovian dynamics of an open quantum system with initial system-reservoir correlations: A nanocavity coupled to a coupled-resonator optical waveguide

In this paper, the exact dynamics of open quantum systems in the presence of initial system-reservoir correlations is investigated for a photonic cavity system coupled to a general non-Markovian reservoir. The exact time-convolutionless master equation incorporating with initial system-reservoir correlations is obtained. The non-Markovian dynamics of the reservoir and the effects of the initial correlations are embedded into the time-dependent coefficients in the master equation. We show that the effects induced by the initial correlations play an important role in the non-Markovian dynamics of the cavity but they are washed out in the steady-state limit in the Markovian regime. Moreover, the initial two-photon correlation between the cavity and the reservoir can induce nontrivial squeezing dynamics to the cavity field.

Entanglement Dynamics of Three Qubits in the Non-Markovian Environments

We consider the entanglement dynamics of three two-level atoms interacting with independent structured non-Markovian reservoirs. The atoms are initially prepared in a mixed multipartite Greenberger—Horne—Zeilinger (GHZ)-type state. Based on the purity and non-Markovian reservoirs, we show that the reservoirs' entanglement can exhibit not only multipartite entanglement sudden birth but also entanglement sudden death, and the revival of atom entanglement is not always accompanied by the disentanglement of reservoirs. Meanwhile, we derive the quantitative criteria for multipartite revival and death phenomena and find multipartite entanglement sudden death and entanglement sudden birth simultaneous apparition time is independent of the initial three-qubit state.

Multi-mode entanglement of N harmonic oscillators coupled to a non-Markovian reservoir

Multi-mode entanglement is investigated in a system composed of N coupled identical harmonic oscillators interacting with a common environment. We treat the problem generally by working with the Hamiltonian without the rotating-wave approximation and by considering the environment as a non-Markovian reservoir to the oscillators. We invoke an N-mode unitary transformation of the position and momentum operators and find that in the transformed basis the system is represented by a set of independent harmonic oscillators with only one of them coupled to the environment. Working in the Wigner representation of the density operator, we find that the covariance matrix has a block diagonal form that can be expressed in terms of multiples of 3 × 3 and 4 × 4 matrices. This simple property allows us to treat the problem to some extent analytically. We illustrate the advantage of working in the transformed basis using a simple example of three harmonic oscillators and find that the entanglement can persist for long times due to the presence of constants of motion for the covariance matrix elements. We find that, in contrast to what one would expect, a strong damping of the oscillators leads to a better stationary entanglement than in the case of a weak damping.

The decoherence dynamics of multipartite entanglement in a non-Markovian environment

We consider four two-level atoms interacting with independent non-Markovian reservoirs with detuning. We mainly investigate the effects of the detuning and the length of the reservoir correlation time on the decoherence dynamics of multipartite entanglement. We find that the time evolution of the entanglement of atomic and reservoir subsystems is determined by a parameter which is a function of the detuning and the reservoir correlation time. We also find that the decay and revival of the entanglement of the atomic and reservoir subsystems are closely related to the sign of the decay rate. We also show that the cluster state is the most robust to decoherence compared with Dicke, GHZ and W states for this decoherence channel.

Entanglement dynamics of multiqubit system in Markovian and non-Markovian reservoirs

We study the entanglement dynamics of three qubits in contact with independent Markovian or non-Markovian reservoirs. The qubits are prepared in two types of GHZ-like or W-like states distinguished by initial excited-state populations. Though belonging to the same GHZ or W class of entanglement, the states with different initial excitations exhibit strikingly different dynamics. In addition, we show that the non-Markovian reservoirs can recover the multiqubit entanglement at instantaneous points or after a finite interval of entanglement disappearance. We also investigate the protection of multiqubit entanglement by the control of excitation emission via the detuning.

Quantum discord in non-Markovian environments

The quantum discord dynamics of two qubits in two independent non-Markovian reservoirs has been investigated. On the condition of resonant interactions, the result shows that the quantum discord has the phenomenon of “revival”. What is more, even in the region where the entanglement is zero, the quantum discord still can reveal the quantum correlations between the two qubits. Considering the detuning, it is interesting to note that the quantum discord can be preserved when the non-Markovian and the detuning conditions are satisfied simultaneously. Finally, an intuitive physical interpretation has been given by the quasimode approach.

Interplay between entanglement and entropy in two-qubit systems

We study the exact entanglement and entropy dynamics of two qubits interacting with a common zero-temperature non-Markovian reservoir. It is a commonly held view that entanglement loss due to environmental decoherence is accompanied by loss of purity of the state of the system. We demonstrate that such an intuitive picture does not always apply: the deterioration of entanglement and purity does not necessarily come together; i.e. revivals of entanglement can be accompanied by deterioration of purity. To complete our investigation on entanglement–mixedness interplay we consider the case of initial mixed states and study how the entanglement dynamics and its revivals are related to both the initial purity and the initial entanglement.

Entanglement measure and dynamics of multiqubit systems: non-Markovian versus Markovian and generalized monogamy relations

In this paper, we first present a simple measure for multiqubit entanglement based on the strategy of bipartite cuts and the measure of negativity. Then, we establish generalized monogamy inequalities and associated partition-dependent residual entanglement (PRE) accounting for arbitrary partitions of a multiqubit system. By virtue of the defined quantities, we investigate the entanglement dynamics of a system of N qubits, either in the Greenberger–Horne–Zeilinger (GHZ)-type state or in the W state, interacting with N independent reservoirs in both Markovian and non-Markovian regimes. We observe entanglement revivals of qubits at instantaneous points of disappearance or after a finite interval of abrupt vanishing due to the memory effect of non-Markovian reservoirs. We also follow the whole entanglement evolution in terms of the PRE to demonstrate the process of transition between the bipartite entanglement of all possible bipartitions and the multipartite entanglement. In particular, we show that the change in time of entanglement formats differs qualitatively for the GHZ-type and W states.

Non-Markovian effect on the quantum discord

We study the non-Markovian effect on the dynamics of the quantum discord by exactly solving a model consisting of two independent qubits subject to two zero-temperature non-Markovian reservoirs, respectively. Considering the two qubits initially prepared in Bell-like or extended Werner-like states, we show that there is no occurrence of the sudden death, but only instantaneous disappearance of the quantum discord at some time points, in comparison to the entanglement sudden death in the same range of the parameters of interest. It implies that the quantum discord is more useful than the entanglement to describe quantum correlation involved in quantum systems.