Research On Acceleration Of Open System Quantum State Dynamics

In quantum computing and quantum information research,how to drive a given initial state to the target state in the shortest time is a fundamental and important issue.This issue involves a number of research areas such as quantum communication,quantum measurement,non-equilibrium thermodynamics,quantum optimal control and so on.The minimum evolutionary time between two distinguishable states is defined as the quantum speed limit time,which is a key factor in characterizing the maximum evolution speed of the quantum states.Recently,people have developed a keen interest in how to achieve the quantum state dynamics speedup.In an actual physical system,the quantum system inevitably interacts with the surrounding environment.Therefore,it is essential to use the concept of quantum speed limit time to investigate the speedup evolution of quantum states in open quantum systems.It is well known that the environment that interacts with the open system is divided into memory and memoryless effects.In a memoryless environment,information flows in a single way,implying that information flows only from the system to the environment,leading to the the Markovian dynamics.However,information can flow in two directions,that is to say,information can flow back from the environment to the system,resulting in non-Markovian dynamics behavior of the quantum system.It has been demonstrated that non-Markovian behavior of the environment can lead to the quantum speedup.However,in the open system,when the system-environment coupling is weak,the system undoubtedly shows Markovian dynamics.Therefore,how to control the environment and transform the system from Markovian dynamics to non-Markovian dynamics,and how to change from no-speedup behavior to speedup behavior are the focus of this paper.First of all,we investigate the detuning damped Jaynes-Cummings model.In the weak coupling regime,the non-Markovian speedup dynamics of the system can be realized by manipulating the detuning and the coupling strength between the qubit and the lossy cavity.In addition,we find that detuning has a dual impact on the system,both to speed up the evolution of the quantum system and to hinder the evolution of the quantum system.Furthermore,the larger the non-Markovianity,the stronger its speedup ability,that is,the shorter the quantum speed limit time is.This result provides a way to achieve non-Markovian speedup control by manipulating the detuning damped Jaynes-Cummings model.Secondly,we investigate the Two-Lorentzian model and the Band-gap model.Based on the original single Lorentzian spectrum,we obtain the Two-Lorentzian model and the Band-gapmodel by adding a new Lorentzian spectrum with positive and negative weight.By manpulating the ratio between two Lorentzian spectrum or the spectrum width of the second Lorentzian spectrum,we can always get the non-Markovian speedup dynamics in the weak-coupling regime.This result shows that in the band-gap model,the non-Markovian speedup dynamics can not be enhanced by adjusting the new Lorentzian parameters.Finally,we investigate the qubit in a hierarchical environment.In the weak coupling regime between the qubit and the first level environment,the dynamics crossovers from the original Markovian to the new non-Markovian and from no-speedup to speedup can be realized by manipulating the number of cavities or the coupling strength between two nearest-neighbor cavities.In addition,in the case of strong coupling between the qubit and the first-level environment,our result revealed that no matter how the second-level environmental parameters are adjusted,compared with the original non-Markovian dynamics,the added second-level environment cannot play a beneficial role on the speedup of the dynamics of the system.In this paper,we get a number of interesting conclusions in our research.We hope these conclusions will help to understand the non-Markovian speedup dynamic.