Decoherence in strongly coupled quantum oscillators

In this paper, we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both regimes of weakly and strongly interacting oscillators from which interesting results arise concerning the coherence properties of the joint and the reduced system states. The strong coupling regime is required to achieve a large frequency shift of the oscillator normal modes, making it possible to explore the whole profile of the spectral density of the reservoirs. We show how the decoherence process may be controlled by shifting the normal mode frequencies to regions of small spectral density of the reservoirs. Different spectral densities of the reservoirs are considered and their effects on the decoherence process are analyzed. For oscillators with different damping rates, we show that the worse-quality system is improved and vice versa, a result which could be useful for quantum state protection. State recurrence and swap dynamics are analyzed as well as their roles in delaying the decoherence process.     

Relaxation- and decoherence-free subspaces in networks of weakly and strongly coupled resonators

We consider a network of interacting resonators and analyze the physical ingredients that enable the emergence of relaxation-free and decoherence-free subspaces. We investigate two different situations: (i) when the whole network interacts with a common reservoir and (ii) when each resonator, strongly coupled to each other, interacts with its own reservoir. Our main result is that both subspaces are generated when all the resonators couple with the same group of reservoir modes, thus building up a correlation (among these modes), which has the potential to shield particular network states against relaxation and/or decoherence.     

Information entropy and entanglement of a superconducting qubit coupled to a cavity field with its spontaneous decay

The quantum entanglement between superconducting qubit and cavity field is described quantitatively in the presence of spontaneous decay. Depending on how how a system is quantum correlated with its environment, the entanglement dynamics between the qubit and cavity is evaluated and investigated during the dissipative process. The motivation based on recent experiments wherein the Cooper box can be used to probe the decay of the resonator superposition state due to environmental decoherence, we theoretically investigate the dynamics of entanglement measured by the negativity. Wehrl entropy and Wehrl phase distribution of a superconducting qubit coupled to a cavity field induced by a superconducting qubit-damping reservoir governed by a master equation.     

Steady bipartite coherence induced by non-equilibrium environment

We study the steady state of two coupled two-level atoms interacting with a non-equilibrium environment that consists of two heat baths at different temperatures. Specifically, we analyze four cases with respect to the configuration about the interactions between atoms and heat baths. Using secular approximation, the conventional master equation usually neglects steady-state coherence, even when the system is coupled with a non-equilibrium environment. When employing the master equation with no secular approximation, we find that the system coherence in our model, denoted by the off-diagonal terms in the reduced density matrix spanned by the eigenvectors of the system Hamiltonian, would survive after a long-time decoherence evolution. The absolute value of residual coherence in the system relies on different configurations of interaction channels between the system and the heat baths. We find that a large steady quantum coherence term can be achieved when the two atoms are resonant. The absolute value of quantum coherence decreases in the presence of additional atom-bath interaction channels. Our work sheds new light on the mechanism of steady-state coherence in microscopic quantum systems in non-equilibrium environments.     

非旋波近似中两能级原子与热库相互作用时原子的消相干特性

两能级原子与外部环境（热库）相互作用时,采用非旋波近似,研究原子与热辐射场单光子和双光子作用过程,利用小系统与库耦合行为的量子理论,计算原子约化密度矩阵非对角元,分析原子状态的消相干特性。     

Dynamics of a Fermi system with resonant dissipation and dynamical detailed balance

The dissipative dynamics of a system of Fermions is described in the framework of a resonance model—the quantum master equation describes two-body correlations of the system with the environment particles. This equation, with microscopic coefficients depending on the exactly known two-body potential between the system and the environment particles, is discussed in comparison with other master equations, obtained on axiomatic grounds, or derived from a coupling with an environment of harmonic oscillators without altering the quantum conditions. The asymptotic solution is in accordance with the detailed balance principle, and with other generally accepted conditions satisfied during the whole time-evolution: Pauli master equations for the diagonal elements of the density matrix, and damped Bloch–Feynman equations for the non-diagonal ones, that we call dynamical detailed balance. For a harmonic oscillator coupled with the electromagnetic field through dipole interaction, a master equation with transition operators between successive levels is obtained. As an application, the decay width of a quantum logic gate is calculated.     

Towards quantum entanglement of micromirrors via a two-level atom and radiation pressure

We propose a method to entangle two vibrating microsize mirrors (i.e., mechanical oscillators) in a cavity optomechanical system. In this scheme, we discuss both the resonant and large-detuning conditions, and show that the entanglement of two mechanical oscillators can be achieved with the assistance of a two-level atom and cavity-radiation pressure. In the resonant case, the operation time is relatively short, which is desirable to minimize the effects of decoherence. While in the large-detuning case, the cavity is only virtually excited during the interaction. Therefore, the decay of the cavity is effectively suppressed, which makes the efficient decoherence time of the cavity to be greatly prolonged. Thus, we observe that this virtual-photon process of microscopic objects may induce the entanglement of macroscopic objects. Moreover, in both cases, the generation of entanglement is deterministic and no measurements on the atom and the cavity are required. These are experimentally important. Finally, the decoherence effect and the experimental feasibility of the proposal are briefly discussed.     

Decoherence Dynamics of a Superconducting Charge Qubit Coupled to a Boson Bath and a Spin Bath

By virtue of a superconducting charge qubit, we derive the off-diagonal matrix operator and investigate the decoherence of the system in different regimes coupled to, respectively, the boson bath and the spin bath. It is found that the two different baths make a bit of difference on the decay of the system at low but finite temperature and the decoherence of the system is most closely linked with the regime as well as the coupling strength. Therefore, by optimizing some reasonable parameters, we can suppress appropriately the decoherence of a given quantum system.     

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin-chain environment with the Dzyaloshinsky-Moriya interaction

We investigate disentanglement dynamics of two coupled qubits and qutrits which interact uniformly to a general XY spin-chain environment with the Dzyaloshinsky-Moriya (DM) interaction. We obtained exact expression of the time evolution operator and analyzed the dynamical process of the decoherence factors. Through explicitly calculating the concurrence and the negativity, we examined disentanglement behaviors of two coupled central spins evolve from different initial pure states, which are found to be nontrivially different from those of the uncorrelated ones, in particular, the enhanced decay of the entanglement induced by quantum criticality of the surrounding environment may be broken by introducing self-Hamiltonian of the central spin system. Moreover, the DM interaction may have different influences on decay of the entanglement depending on the strength of the system-environment coupling, the anisotropy of the environmental spin chain and the intensity of the transverse magnetic field, as well as the explicit form of the initial states of the central spin system.     

Rate of Decoherence for an Electron Weakly Coupled to a Phonon Gas

We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction.     

Dynamics of microcavity polaritons in the Markovian limit

A master equation for the reduced density matrix of the microcavity polaritons coupled with the reservoir of high energy excitons is derived. It is allowed both the polaritons and the excitons to be self-interacting systems. Long time asymptotic properties of the polariton population is studied in the whole range of the reservoir temperatures and the corresponding decoherence effects are reported.     

Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

Dissipative Dynamics of Quantum Discord of Two Strongly Driven Qubits

The exact dynamics of quantum discord (QD) of two strongly driven qubits, which are initially prepared in the X-type quantum states and inserted in two independent dissipative cavities or in a common dissipative cavity, are studied. The results indicate that both in the two cases, the evolution of QD is independent of the initial cavity state. For the two independent dissipative cavities, it is found that the phenomenon of sudden transition between classical and quantum decoherence exists and the transition time can be greatly delayed by suitably choosing the initial state parameter of the two qubits, the cavity mode-driving field detunning and the decay rate of the cavity. For the common dissipative cavity, it is shown that for some initial states of the two qubits, the QD can increase for a finite time at first, and then it decreases to a steady value, while for some other initial states, the QD can increase monotonously or with oscillation till a stable value is reached. Moreover, the creation of QD for the two qubits in a common cavity is discussed.     

Environment-induced decoherence I. The Stern-Gerlach measurement

A dynamical model for the collapse of the wave function in a quantum measurement process is proposed by considering the interaction of a quantum system (spin -1/2) with a macroscopic quantum apparatus interacting with an environment in a dissipative manner. The dissipative interaction leads to decoherence in the superposition states of the apparatus, making its behaviour classical in the sense that the density matrix becomes diagonal with time. Since the apparatus is also interacting with the system, the probabilities of the diagonal density matrix are determined by the state vector of the system. We consider a Stern-Gerlach type model, where a spin-1/2 particle is in an inhomogeneous magnetic field, the whole set up being in contact with a large environment. Here we find that the density matrix of the combined system and apparatus becomes diagonal and the momentum of the particle becomes correlated with a spin operator, selected by the choice of the system-apparatus interaction. This allows for a measurement of spin via a momentum measurement on the particle with associated probabilities in accordance with quantum principles.     

Searching for robust quantum memories in many coupled oscillators

The relation between microscopic symmetries in the system-environment interaction and the emergence of robust states is studied for many linearly coupled harmonic oscillators. Different types of symmetry, which are introduced into the model as terms in the coupling constants between each system?s oscillator and a common reservoir, lead to distinct robust modes. Since these modes are partially or completely immune to the symmetric part of the environmental noise, they are good candidates for building quantum memories. A comparison of the model investigated here, with bilinear system-reservoir coupling, and a model where such coupling presents an exponential dependence on the variables of interest is performed.     

三量子位系统的消相干和退纠缠

基于多谐振子热库环境模型,采用求解非马尔可夫近似主方程方法,研究了三量子位系统由于相对位相变化引起的消相干和退纠缠.计算得到了初始态为GHZ-class态、W-class态和WGHZ-class态在演化过程中的消相干和退纠缠时间尺度.结果表明,对初始GHZ-class态,相干性全部丧失,退纠缠完全发生,纠缠度变为0;对初始W-class态,相干性和纠缠度被保持;对初始WGHZ-class态,消相干部分发生,纠缠首先随时间变化最后达到一个渐近值.     

Entropy Exchange and Entanglement in Superconducting Charge Qubit Inside a Resonant Cavity with Intrinsic Decoherence

By considering the intrinsic decoherence effect, we investigate the entropy exchange and entanglement in the interacting system of a superconducting charge qubit coupled to a single-mode optical cavity. We found that although the intrinsic decoherence leads to an irreversible evolution of the interacting system due to a suppression of coherent quantum features through the decay of off-diagonal matrix elements of the density operator, and has an apparently influence on the partial entropies of the two-component subsystems, it dose not destroy entropy exchange behavior. In addition, the lower bound of the concurrence, as the measure of entanglement of the coupling system, is calculated. It is shown that the evolution of entanglement is sensitive to the change of the intrinsic decoherence.     

腔场初始态对两量子比特空间退相干的影响

研究了两个二能级原子与一个单模腔场的相互作用中,腔场的不同初始态对原子间相对位置退相干的影响。从描述原子间相对位置状态的约化密度矩阵出发,假设原子间相对位置为两个高斯波包的叠加态,讨论了当腔场初始态分别为热态、Fock态和压缩态情况下,原子与光场的相互作用对两原子间相对位置相干性的影响。发现腔场的初始态不同,原子间相对位置的退相干情况有所不同。当腔场初始态为热态或Fock态时,原子间相对位置的相干性会周期性的衰减和回复,而当腔场初始态为压缩态时,原子间相对位置会出现部分退相干,且退相干程度与原子间相对位置的大小成余弦变化关系。     

Dissipation, decoherence and preparation effects in the spin-boson system

The dynamics of the reduced density matrix of the driven dissipative two-state system is studied for a general diagonal/off-diagonal initial state. We derive exact formal series expressions for the populations and coherences and show that they can be cast into the form of coupled nonconvolutive exact master equations and integral relations. We show that neither the asymptotic distributions, nor the transition temperature between coherent and incoherent motion, nor the dephasing rate and relaxation rate towards the equilibrium state depend on the particular initial state chosen. However, in the underdamped regime, effects of the particular initial preparation, e.g. in an off-diagonal state of the density matrix, strongly affect the transient dynamics. We find that an appropriately tuned external ac-field can slow down decoherence and thus allow preparation effects to persist for longer times than in the absence of driving. Received 23 October 1998 and Received in final form 26 February 1999