Research On Disorder Effect Of One-Dimensional Cold Atom System

The cold atom system has been an excellent experimental platform for its outstanding maneuverability since it was implemented in the laboratory.Disorder effect has become a hot topic in recent years after it is realized in cold atom system,because disorder effect can lead to many interesting and counterintuitive physical phenomena.In this paper,we investigate the effect of disorder on the coherence of small quantum systems in cold atom systems.Based on second quantization,Bose-Hubbard model is introduced,and the coherence of the system is investigated by numerical simulation and theoretical analysis in this model.Our work is divided into two main parts.In the first part,we study the dynamic evolution of coherence in a disordered double-well system,focusing on the manipulating of coherence by time-dependent drivers of interaction.By adjusting the frequency of the time-dependent driver,we find a method to improve the coherence of the disordered system,and give the coherence phase diagram of the driving amplitude and driving frequency.Based on the high frequency approximation,a coherent correlation function is obtained by solving the Schrodinger Equation.Finally,in the resonant and non-resonant region,the relationship among coherence,driving amplitude and driving frequency is discussed.In the second part,we investigate the influence of disorder effect on the coherence of the ground state in a ring-shaped triple-well system with dipole-dipole interaction,simple in order to study the influence of polarization direction of coherence.Two special polarization directions are selected to study the coherence of the system.In these two cases,phase coherence diagrams of the on-site interaction and the dipole interaction are given.Three distinct phases are differentiated in the phase diagram.We give the reasons of the three phase boundary and the explanation of the internal structure of the phase by theoretical approximation.Finally,the relationship between the average particle number and coherence is obtained.