Entanglement Resonance And Quantum Speedup Mechanisms Of Periodically Driven Systems

Quantum entanglement is a novel characteristic that distinguishes quantum physics from classical physics.It is a basic resource for the development and application of modern quantum engineering.How to measure,control,and create entanglement is an important topic in current quantum information science.In recent years,researchers have proposed systems such as electron spin,semiconductor quantum dots,and cavity quantum electrodynamics to prepare entangled states.In this thesis,we will explore the use of periodic driving to prepare entangled states.Furthermore,the inevitable impact of the environment on the system leads to the decoherence effect of the system,which to a large extent restricts the preparation of quantum entanglement and the realization of related quantum engineering schemes.In this thesis,we will also explore the controllability of periodic driving to open quantum systems.First,we study the energy spectral features of the external field-driven quantum Rabi model and the entanglement properties of their corresponding eigenstates.In the rotating wave approximation,with the help of perturbation theory,we find that the original degenerate energy levels are split,namely,the energy levels avoid crossing due to the external field.The von Neumann entropy of the corresponding point has interesting entanglement resonance features,and its change depending on the light-matter coupling strength and the driving amplitude,which are intrinsically related to the structure of the energy spectrum of the model.Next,we numerically explore the entanglement features of the quantized light fields and the statically driven two-level system,namely the entanglement resonance phenomenon in the asymmetric quantum Rabi model.As the photon-atom coupling strength increases,interesting entanglement resonance valleys emerge,and the peaks appear as the driving amplitude increases.It is shown that both entanglement resonances are caused by the level-avoided crossings of the relevant eigenenergies.In sharp contrast to the quantum Rabi model,the entanglement of the asymmetric quantum Rabi model drops to zero in the strong coupling region,except that the driving amplitude is half-integer times of the photon frequency.Further,we explore the entanglement preparation of the periodically driven Rabi model.Entanglement is prepared by applying a periodic driving field to the system.The Hamiltonian of an autonomous quantum system has a certain energy eigenvalue.If the system is in this eigenstate,any properties of the system will not change with time.By adjusting the parameters of the system,the eigenstate of the system can be adjusted to be entangled.Here,the above scheme is extended to the periodically driven quantum system,and the entanglement is prepared by applying a periodic driving field to the system.According to Floquet theory,there will be a set of orthogonal complete instantaneous basis vectors called Floquet states for periodic systems and their corresponding eigenvalues playing the same role as energy eigenstates and eigenenergy in autonomous quantum systems.By adjusting the driving parameters,one or several Floquet states will remain entangled throughout the driving cycle.When the system is prepared in this state,the system will always maintain its entanglement over time.We apply a periodic driving field to the two weakly coupled two-level systems,and analyze the resonance phenomenon of average entanglement induced by the periodic driving.Further studies reveal that the entanglement resonance is caused by the avoided level crossing of the quasienergy spectrum.Periodic driving induced quasi-level crossover avoidance and its resulting entanglement resonance provide important technical solutions for entanglement preparation of quantum systems.Second,we study the efficient role of periodically driven optical lattice in preparing entanglement for ultracold atoms.The optical lattice is formed by the intersection of one or several laser beams to form a spatial periodic potential.Its advantage is the controllability to the shape and symmetry of the lattice,and the interaction strength between atoms by adjusting the laser wavelength,polarization,and position layout.By periodically driving the interaction between the atoms in the potential well,the entanglement resonance is found.Its intrinsic relationship with the avoided level crossing in the quasienergy spectrum is further revealed.The analysis shows that the average entanglement entropy of multi-particle system has a good role with the quantum phase transition and quantum fluctuations of the system,which provides an effective theoretical basis for the entanglement characteristics of multi-particle quantum system.Finally,we study the decoherence effect of the open system by the external periodic driving.Through the periodic modulation of the composite system composed of two-level atoms and the bosonic environment.It is found that when the bound state is formed in the energy spectrum of the composite system composed of the system and the environment,the dynamic evolution of the system changes significantly.By describing the correspondence between the quantum speed limit of the system and the characters of the Floquet quasienergy spectrum,it is found that the formation of bound states in the Floquet quasi energy spectrum of the composed system plays a decisive role in the appearance of quantum speedup.When the system does not form a Floquet bound state,the relative quantum speed limit of the system gradually converges to a non-zero finite value,indicating that the quantum speedup capacity of the system is limited.Once the Floquet bound state is formed in the quasi-energy spectrum,the relative quantum speed limit will approach zero,which indicates that the system has a strong speedup potential.These results are helpful to achieve more flexible experimental acceleration of open quantum systems,and also provide inspiration for the study of non-equilibrium states.Through systematic study on periodic driving,we found that the avoided level crossing in the quasi-energy spectrum induced by periodic driving and the resulting entanglement resonance have positive significance for the entanglement preparation of quantum systems.The results that the formation of bound states in the Floquet quasienergy spectrum has a decisive effect on the quantum acceleration of open systems.It not only provides a theoretical guidance for the realization of quantum acceleration in experiments,but also helps to enrich our understanding on the non-equilibrium statistical physics.