Decoherence and dynamical entropy generation in quantum field theory

We formulate a novel approach to decoherence based on neglecting observationally inaccessible correlators. We apply our formalism to a renormalised interacting quantum field theoretical model. Using out-of-equilibrium field theory techniques we show that the Gaussian von Neumann entropy for a pure quantum state increases to the interacting thermal entropy. This quantifies decoherence and thus measures how classical our pure state has become. The decoherence rate is equal to the single particle decay rate in our model. We also compare our approach to existing approaches to decoherence in a simple quantum mechanical model. We show that the entropy following from the perturbative master equation suffers from physically unacceptable secular growth.     

Decoherence of quantum Brownian motion in noncommutative space

The decoherence of a harmonic oscillator under two-dimensional quantum Brownian motion on a noncommutative plane is investigated. The interaction with the environment is considered by two separate models so-called coupled and uncoupled. The two-dimensional master equation and its noncommutative counterpart are derived for both employed models. The rate of the linear entropy (predictability sieve) is chosen as a criterion to investigate the purity in the presence of the space noncommutativity. Besides, a two-dimensional charged harmonic oscillator on a plane which is imposed by a perpendicular magnetic field is introduced as a realization of our model. Therefore, our approach provides a formalism to investigate the influence of the magnetic field on the decoherence of the pure states. We show that in the high magnetic field limit the rate of the decoherence will be decreased.     

Collective quantum decoherence induced by qubit-electron interaction

We investigate a model of quantum register composed of N qubits coupling with itinerant electrons by adopting the Born-Markov master equation. Decoherence induced by this coupling is studied for various initial states. By solving the master equation for N=4 with the numerical integration, we obtain time evolution of fidelity and linear entropy of the register. The decoherence rate of this model is proportional to ²|J^′| with J^′ being the exchange coupling strength of electrons and qubits. We also investigate the decoherence free subspace which provides a possible routine of applications in quantum computation.     

时间无卷积广义主方程中核函数的精确解和高阶微扰展开:在自旋-玻色模型和激发态能量转移中的应用

The time-convolutionless (TCL) quantum master equation provides a powerful tool to simulate reduced dynamics of a quantum system coupled to a bath. The key quantity in the TCL master equation is the so-called kernel or generator, which describes effects of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion (HEOM) and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with different sets of parameters, to investigate the convergence of the high order expansions of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.     

Entanglement entropy, decoherence, and quantum phase transitions of a dissipative two-level system

The concept of entanglement entropy appears in multiple contexts, from black hole physics to quantum information theory, where it measures the entanglement of quantum states. We investigate the entanglement entropy in a simple model, the spin-boson model, which describes a qubit (two-level system) interacting with a collection of harmonic oscillators that models the environment responsible for decoherence and dissipation. The entanglement entropy allows to make a precise unification between entanglement of the spin with its environment, decoherence, and quantum phase transitions. We derive exact analytical results which are confirmed by Numerical Renormalization Group arguments both for an ohmic and a subohmic bosonic bath. The entanglement entropy obeys universal scalings. We make comparisons with entanglement properties in the quantum Ising model and in the Dicke model. We also emphasize the possibility of measuring this entropy using charge qubits subject to electromagnetic noise; such measurements would provide an empirical proof of the existence of entanglement entropy.     

Quantum walks: Decoherence and coin-flipping games

We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first mechanism drives the system towards a classical diffusive behavior. This is used to build new quantum games, similar to the spin-flip game. The second mechanism involves two different possibilities: (a) All the quantum walk links have the same probability of being broken. (b) Only the quantum walk links on a half-line are affected by random breakage. In case (a) the decoherence drives the system to a classical Markov process, whose master equation is equivalent to the dynamical equation of the quantum density matrix. This is not the case in (b) where the asymptotic global chirality distribution unexpectedly maintains some dependence with the initial condition. Explicit analytical equations are obtained for all cases.     

Decoherence induced by zero-point fluctuations in quantum Brownian motion

We show a completely analytical approach to the decoherence induced by a zero temperature environment on a Brownian test particle. We consider an Ohmic environment bilinearly coupled to an oscillator and compute the master equation. From diffusive coefficients, we evaluate the decoherence time for the usual quantum Brownian motion and also for an upside-down oscillator, as a toy model of a quantum phase transition.     

原子分子光子系统的耗散相互作用和退相干

原子分子系统与量子化的电磁场或光子模式耦合的系统是非相对论量子力学理论研究和实验研究的主要对象和模型. 现实系统必然与外界环境耦合,且即便原子隔绝较好、光学腔壁品质因子足够高,原子系统也不等价于少数几个能级构成的简单模型：它仍然有不为零的几率跃迁到不可控的能级空间、与原子相互作用的自由空间真空场的量子效应也必须考虑. 本文将结合开放量子系统理论的基本要素与原子光子的基本模型,对原子分子系统在电磁场中发生的耗散以及量子退相干过程做简单综述,并重点介绍描述量子系统退相干过程的主流理论工具——主方程.     

Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameterγ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rateγ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.     

Growing Classical and Quantum Entropies in the Early Universe

Following the idea that the global and local arrow of time has a cosmological origin, we define an entropy in the classical and in the quantum periods of the universe evolution. For the quantum period a semi-classical approach is adopted, modelling the universe with Wheeler-De Witt equation and using WKB. By applying the self-induced decoherence to the state of the universe it is proved that the quantum universe becomes a classical one. This allows us to define a conditional entropy which, in our simplified model, is proportional to e ^{2γ t} where γ is the dumping factor associated with the interaction potential of the scalar fields. Finally we find both Gibbs and thermodynamical entropy of the universe based in the conditional entropy.     

Entropy and correlators in quantum field theory

It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observer's ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.     

Qubit-assisted squeezing of mirror motion in a dissipative cavity optomechanical system

In this study, we investigate a hybrid system consisting of an atomic ensemble trapped inside a dissipative optomechanical cavity assisted with perturbative oscillator-qubit coupling. Such a system is generally very suitable for generating stationary squeezing of the mirror motion in the long-time limit under the unresolved sideband regime. Based on the master equation and covariance matrix approaches, we discuss in detail the respective squeezing effects. We also determine that in both approaches, simplifying the system dynamics with adiabatic elimination of the highly dissipative cavity mode is very effective. In the master equation approach, we find that the squeezing is a resulting effect of the cooling process and is robust against thermal fluctuations of the mechanical mode. In the covariance matrix approach, we can approximately obtain the analytical result of the steady-state mechanical position variance from the reduced dynamical equation. Finally, we compare the two approaches and observe that they are completely equivalent for the stationary dynamics. Moreover, the scheme may be useful for possible ultraprecise quantum measurement that involves mechanical squeezing.     

Comparison between decoherence time for a two-state spin ½ system with its corresponding quantum retrieval period

The evolution of a two-state quantum system (a spin ½ particle) in both the framework of standard quantum mechanics and under the decoherence regime is considered. The former approach on this issue is the well-known quantum flipping process of a dichotomic system subjected to a time-dependent magnetic field. In the latter approach, the Spin-Boson model is utilized to describe the interaction of system with its environment and the Born-Markov master equation is derived to obtain the decoherence time. It is possible to show that under certain conditions, one may find a potential conflict between the predictions of decoherence theory and the result observed in a typical quantum flipping experiment.     

Robustness and diffusion of pointer states

Classical properties of an open quantum system emerge through its interaction with other degrees of freedom (decoherence). We treat the case where this interaction produces a Markovian master equation for the system. We derive the corresponding distinguished local basis (pointer basis) by three methods. The first demands that the pointer states mimic as closely as possible the local nonunitary evolution. The second demands that the local entropy production be minimal. The third imposes robustness on the inherent quantum and emerging classical uncertainties. All three methods lead to localized Gaussian pointer states, their formation and diffusion being governed by well-defined quantum Langevin equations.     

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.     

Replacing energy by von Neumann entropy in quantum phase transitions

We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.     

Resilient quantum computation in correlated environments: a quantum phase transition perspective

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by quantum error correction using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for a long time and/or a large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the "threshold theorem" of quantum computing is rephrased as a dimensional criterion.     

Quantum theory of irreversibility

A generalization of the Gibbs–von Neumann entropy is proposed based on the quantum BBGKY (Bogolyubov–Born–Green–Kirkwood–Yvon) hierarchy as the non-equilibrium entropy for an N$N$-body system. By using a generalization of the Liouville–von Neumann equation describing the evolution of a density superoperator, the entropy production for an isolated system is calculated, being non-zero in general. The existence of a non-zero entropy production allows us, following the procedure of non-equilibrium thermodynamics to introduce a master matrix for which a microscopic expression is obtained. After this, as a test of our theory the quantum Boltzmann equation is derived in terms of a transition superoperator related to this master matrix.     

Mean-Field Dynamics of a Two-Mode Bose-Einstein Condensate Subject to Decoherence

We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherenee （or particle loss）. Starting from the full many-body dynamics described by the master equation, an effective Gross- Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.