Quantum Speed Limits In Open System

How fast can a quantum system evolve? This is one of the fundamental problems involved in all areas of quantum physics,which determines the shortest duration of the evolution of a physical process.Quantum speed limit time(QSLT)is defined as the minimal time that a system needs to evolve from a quantum state to the final distinguishable state,which can reflect the maximal speed of evolution of a quantum system.During the past decades,the study of the QSLT has been mainly focused on closed quantum systems.Since all systems are unavoidably connected to their surroundings,quantum coherent superposition is easily affected by external environment resulting in decoherence.Therefore,the study of quantum open system speed limit problem and method to improve the quantum system evolution speed against decoherence,for completing the manipulation of quantum state and realizing the logic operations within a limited time,is of great significance.In this thesis,we mainly investigate the quantum speed limit in open quantum systems and the entire thesis consists of the following three parts.In the first part,we study the quantum speed limit time of an open system and find it can be useful to highlight the quantum phase transition(QPT).We investigate the QSLT of a coupled system consisting of a central spin and its surrounding environment,and the environment is described by a general XY spin-chain model.For initial pure state,we find that the local anomalous enhancement of the QSLT occurs near the critical point.In addition,we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point.These anomalous behaviors in the critical vicinity of XY spinchain environment can be used to indicate the quantum phase transition point.Especially for the XX spin-chain environment,we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point.In this case,the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field,while the QSLT can still witness the quantum phase transition.So,the QSLT provides a further insight and sharper identification of quantum criticality.In the second part,we study the speed-up role of dynamical decoupling in an open system.We apply a train of Bang–Bang pulses to two central spins coupled to their own XY spinchain environment,and find that the evolution speed of the system can be effectively modulated by a judicious choice of the pulse frequency.We show that the fast Bang–Bang pulses can suppress the system evolution,which manifests the quantum Zeno effect.In contrast,with the increasing of the pulse interval time,the Bang–Bang pulses can enhance the decay of the quantum speed limit time and induce the speed-up process,which displays the quantum anti-Zeno effect.In addition,we show that the random pulses can also induce the speed-up of quantum evolution.In the third part,we investigate the influence of DM-interaction on the evolution speed of the center spin system.Our results show that,with increasing the strength of DM-interaction of spin-chain environment,the critical behavior of the quantum speed limit at the phase point becomes more prominent.It implies that the DM-interaction can enhance the ability of the quantum speed limit for indicating the QPT.In addition,we consider the quantum speed limit for an arbitrary time-evolution state in the whole dynamics process and find that DMinteraction can play a role in the speed-up quantum system evolution.In the last part,we study the effect of environment temperature on the evolution of the center system speed.We find that,under the limited temperature environment,the quantum speed limit still be a good indicator of the quantum phase transition.However,as the temperature increases,the critical behavior of the quantum speed limit weakened.In addition,we investigate the quantum speed limit in the whole dynamics process and find the quantum system evolution was accelerated with the increase of temperature.