The Study Of Topological Properties And Decoherence In A Periodically-driven Double Kicked Rotor System

The study of topological phase becomes a hot topic in rencent years.The band structure of physical systems,which include static and periodically-driven system,determines whether there exist non-trival topological phases.Especially periodically-driven system displays richer topological phases.In this paper,some basic concepts about Floquet system,topology invariant,discrete-time quantum walk and the behaviors of discrete-time quantum walk achieved by a periodically-driven single kicked rotor are firstly introduced.Based on these,the energy spectrum and the topological phase transition of double kicked rotor model are studied.The effects of decoherence on dynamical evolution of one-dimensional diatomic chain complex momentum lattice model are also considered.The physical process,loading atoms with two hyperfine level into a periodic optical lattice and meanwhile using two standing wave laser pulses with same frequency to act atoms in a pulse period,is described as a double kicked rotor model.Basing on its Hamiltonian,we obtain Floquet operator and take it as a quantum walk with two conditional transition operators.By caculating the momentum standrad deviation of the double-step quantum walk,we find that it is always lower than that of single-step quantum walks.This result has nothing to do with the changing values of two-kicked-rotor parameters.Adding the coin operator with adjustable parameters to Floquet operator to change the coin states after each single-step evolution,the effects of adjustable parameters on the topological properties of system are studied.Floquet quasi-energy spectrum and topological winding number are obtained to characterize topological properties of system.We find that there exist topological phases protected by the chiral symmetry.With the variations of the coin parameters,these topological phases can be characterized by the large winding numbers.Furthermore,we calculate numerically Floquet spectrum and the eigenvectors of system in a finite momentum space.It isobserved that zero and ? energy edge states exist at the boundary.The number of edge states is consistent with the topological winding numbers,which indicates that the system satisfies with the bulk-boundary correspondence.When the initial states of system is given,the Von Neumann entropy under different parameters is numerically calculated.It is shown that the lager the parameter value,the higher the entanglement between momentum and spin degrees of freedom.When the time interval between two standing wave laser pulses is not equal to half of resonance period,the system determined by Floquet operator is equivalent to a complex lattice model of one-dimensional diatomic chain in momentum space.Odd and even atom sites,being similar to pseudspin,can be regared as the coin degree of freedom in quantum walk.We calculate the mean displacement of quantum walk to describe the topological phase transition of system.Further considering the decoherence effect caused by the continuous measurement,it is found that with the increase of the decoherence probability,the momentum distribution probability of the particles decreases exponentially,and the extended width becomes smaller.The extended state gradually overlaps with the topologically protected edge state.As a result,the quantum behaviors of system transition to the classical behaviors.