Effects Of Classical Drives On The Dynamics Of Quantum Systems

In the actual quantum physical system,quantum system will inevitably interact with the external environment.The control of the dynamics of the open systems is an important topic in the field of quantum information.On the basis of the rapid development of quantum information technology,people increasingly need a safe,efficient and low loss quantum state evolution process.Quantum speed limit time,as the shortest time to describe the evolution between the initial state and the target state,has been attracted much attention in recent years.It can be used to characterize the maximum evolution speed of the quantum system dynamics process.Therefore,the research on the potential speedup evolution of open system quantum state based on quantum speed limit time is also a key issue.On the other hand,the non-Markovianity of the system as a measure of the environmental information return ability is often analyzed together with the quantum speed limit time.But the relationship between the two is controversial.In this paper,the evolution of a single qubit in different Markovian channels and the dynamics process of spin-magnet model are studied respectively.Quantum speed limit time and non-Markovianity are calculated respectively,and the relationship between them is analyzed.1.The quantum evolution speed of quantum state can never be accelerated in the Markovian regime without any operators on the system.Considering three Markovian noisy channels(the phase-flip channel,the amplitude damping channel and the depolarizing channel),we propose a scheme of speedup evolution of the system by controlling an external unitary coherent driving operator on the system.It is shown that,in the presence of the coherent driving,no-speedup evolution can be transformed into quantum speedup evolution in the Markovian dynamics process.Additionally,under the fixed coherent driving strength in the above three noisy channels,the best way to achieve the most degree of quantum speedup for the system has been acquired by rotating the system with appropriate driving direction angles,respectively.Finally,we conclude that the reason for this acceleration is not the non-Markovian dynamical behavior of the system but due to the oscillation of geometric distance between the initial state and the target final state.2.We firstly consider the dynamics control of a spin-1/2 system simultaneously interacting with two magnets,which act as measuring apparatuses of two different spin components.Then we also study in detail the evolution of a classical driven spin-1/2 system coupled with a magnet.For these two models,two dynamical crossovers of the spin system,from Markovian to non-Markovian dynamics and from no-speedup evolution to speedup evolution,can be controlled.Comparing to the previous quantum speedup scenarios by the controllable non-Markovianity,in our spin-magnet schemes the stronger non-Markovianity does not necessarily lead to the quantum speedup dynamics process of the spin system.By comprehensive analysis of the conclusions of these two models,we can realize the transformation from no-speedup evolution phenomenon to speedup evolution phenomenon,and we know that non-Markovian regime is not a necessary condition for the quantum evolution process to produce speedup.