Quantum Decoherence Dynamics In Nonequilibrium Environments

Since the establishment of quantum mechanics in the early 20th century,we have made revolutionary changes in our understanding of the microscopic phenom-ena,which is unprecedented in the development of the history of natural sciences.The problems of open quantum systems have been around since the beginnings of the establishment of quantum mechanics.In the realistic world,a quantum system is considered to be an open quantum system,unavoidably coupled to a surround-ing environment that induces the loss of coherence during the dynamical evolution.Theoretical and experimental researchers have mainly focused on the community:How to preserve quantum coherence and how to suppress and control dynamical decoherence.In contrast to the case of a closed system,the dynamics of an open quantum system cannot be generally represented in terms of a unitary time evolu-tion.The dynamics of open quantum systems can be described,for a long time,within the Markov approximation,by master equations in the Lindblad structure.In recent years,the investigations on the non-Markovian quantum dynamics have increasingly drawn attention,due to the advent of experimental capability to ob-serve and control open quantum systems at different time,length scales and energy-ranges.However,because of the difficulty in treating non-Markovian dynamics,on-ly a few exact non-Markovian master equations have been derived based on different approaches.Quantum speed limits(QSLs)are the lower bounds on the minimal evolu-tion time between two distinguishable states of a quantum system,which would have potential applications in understanding how to quantify and manipulate quan-tum coherence and in protecting quantum information against decoherence induced by environmental noise.For an isolated quantum system under unitary evolu-tion,two independent bounds on this minimum evolution time were established by Mandelstam-Tamm(MT)linked to the variance of the energy of the system and by Margolus-Levitin(ML)associated with the average energy of the system.Re-cently,generalized ML and MT types of QSL bounds for an open quantum system under nonunitary dynamical evolution have been derived based on different geo-metric measures for the distinguishability between the initial and final states of the system.The ratio between the QSL time and driving time estimates the potential capacity of speeding up quantum dynamical evolution.When the ratio equals one,there is no potential capacity for quantum dynamical evolution speedup,while for other cases the smaller the ratio is,the greater the potential capacity will be.Previously,most theoretical investigations on the dynamical decoherence of open quantum systems have assumed that the environments have an infinite number of uncontrolled degree of freedom and are in equilibrium with both stationary and Markov statistical properties.However,with the advent of experimental technique,it is shown that,in some situations,the nonequilibrium feature of the environment becomes dominant.For example,transient and ultrafast dynamical processes in physical or biological systems may occur on sufficiently short time scales while the initial nonequilibrium states induced by the coupling between the system and its surroundings may not have the chance to return to equilibrium.On the other hand,a quantum system may interact with composite or structured environments where the interaction between the environments plays an essential role in the decoherence dynamics of an open quantum system.In this situation,the nonequilibrium feature of the environment with nonstationary statistics and the environmental memory effect are necessary to be taken into extensive consideration.Environmental effects on an open quantum system can be classified into two aspects:transition between quantum states and loss of phase coherence induced by dissipative and pure decoherence environments.There have been well-established investigations on the dynamical speedup of evolution of a quantum system with en-ergy dissipation in an equilibrium environment theoretically,and the environment-assisted speedup of dynamical evolution is realized by controlling the environment experimentally.The connection has been investigated between QSLs and entan-glement and non-Markovianity:It was shown that entanglement can speed up the dynamical evolution of a closed composite system;It was also confirmed that the non-Markovian effect of the open system dynamics is the unique condition for speeding up quantum dynamical evolution in the long driving time limit while it is a necessary but not sufficient condition to speed up the dynamical evolution of the quantum system within a given driving time.However,the mechanism for the speedup of quantum evolution in a pure decoherence environment is unknown.What puzzles us is:for an isolated quantum system under unitary dynamics,the speedup of dynamical evolution is closely related to the energy of the system where-as the dynamical speedup is no longer associated with the energy of the system for an open quantum system under nonunitary evolution.Therefore,we think that the mechanism for the speedup of dynamical evolution of an open quantum system has not been fully explained.Many important questions need to be discussed in detail:How does a nonequi-librium environment affect the dynamical decoherence of a quantum system and the environmental backaction of coherence;how does the environmental memory effect influence the decoherence dynamics of the quantum system and the coherent backaction from the environment?How can we relate the QSLs with dynamical de-coherence,what is the mechanism for the dynamical speedup under nonequilibrium dccohercnce processes,and how can we speed up the quantum dynamical evolution in a nonequilibrium environment and so on.So,in this thesis,we investigate and discuss the relevant questions mentioned above.The thesis is divided into six chapters and organized as followsIn the first chapter,we first introduce the background of our research,and then make a brief introduction of the process of dynamics of open quantum sys-tems.In the next,we describe and the status of the investigations on the quantum dynamics in nonequilibrium environments.We also review the quantum speedup of dynamical evolution of open quantum systems.Then,We introduce the theoretical investigations to be carried out in the end of this chapter.In the second chapter,we give an introduction of open quantum systems in detail.We first introduce some basic knowledge of stochastic processes based on classical theory of probability.Next,we introduce two approaches of treating open quantum systems and the general derivation of the dynamical evolution of reduced density matrix.Then we make a brief introduction of the quantification of the non-Markovian behavior in open quantum system dynamics.In the third and forth chapters,we develop two approaches to obtain the exact quantum dynamical equation in the presence of nonstationary non-Markovian ran-dom telegraph noise,namely,closed dynamical equation and generalized stochastic Liouville equation,respectively.Then,we discuss the influence of nonequilibrium environments on the dynamical evolution of the quantum system.In the fifth chapter,based on the trace distance in quantum space,we establish the generalized ML and MT types of QSL bounds and we relate the QSL time with both the energy of the system the decoherence dynamics associated with the the unitary and nonunitary parts of the dynamical evolution.Then,we illustrate the mechanism for the dynamical speedup of evolution in nonequilibrium environments.In the last chapter,we give the brief conclusions drawn from the present study and we give the outlook on the future investigation.