Stability Of Bose-einstein Condensate In Parametrically Modulated One-dimensional Optical Lattices

In recent years,periodical modulation of Bose-Einstein condensate(BEC)has attracted considerable attention.Particularly,the dynamics and stability of periodically modulated BEC in optical lattices have became a hot research topic.There are many interesting physical phenomenon in periodically modulated BEC in optical lattices,such as dynamics localization,quantum phase transition between the boson superfluid state and the Mott insulator state,the realization of topological band structures,artificial magnetic field,artificial spin orbit coupling and artificial dimension.Recently,periodic modulation of the external harmonic potential affect the dynamic stability of BEC in optical lattice is studied.It is found that periodic modulation of the harmonic potential can significantly change the stability of BEC.In fact,there are still long-range dipole interactions in BEC.However,the periodic driving of the system with both contact interaction and dipole interaction still open question.Therefore,the first work emphatically discuss the influence of periodic modulation of harmonic potential on dynamic stability of dipole BEC in optical lattice.On the other hand,the phase transition and dynamics of the bosonic magnetic ladder with artificial magnetic field have been attracted extensive attention.It is found that there exists rich phase transformation and dynamic characteristics in the system,such as chiral flow and Meissner phase,which has great significance to understand superconductivity in condensed matter physics.However,The stability of bosonic magnetic ladders under modulated harmonic potential is still not clear.So,the second work is focused on how the modulated harmonic potential affect the stability of bosonic magnetic ladders system.The structure of this dissertation is as follows:Firstly,the background knowledge closely related to this dissertation is introduced,including foundation theory of BEC in optical lattice,dipole BEC,dynamics and stability of periodically modulated BEC,and the research status and the existing problems on the phase transition and dynamics of the bosonic magnetic ladders.Secondly,we study the stability properties of dipole BEC in a deep onedimensional optical lattice with an additional external parameter modulated by harmonic trap potential.Through variational analysis and numerical simulation,we solve a dimensionless nonlinear discrete Gross-Pitaevskii equation with both the short-range contact interaction and the long-range dipole-dipole interaction.The motion differential equation is given by the variational method,which shows how parameter of system affects the width of the condensate.A critical condition controlling the stability of the condensate is obtained by theoretical calculation.Through the research,it is found that the stability of the system can be regulated by coupling the dipole interaction,the contact interaction and the periodic drive strength.In addition,the breather dynamics,the diffusion dynamics and the attractive interaction-induced-trapped dynamics are observed.By performed a numerical simulation for GP equation,the analytical results are confirmed.Thirdly,the stability of bosonic ladders with artificial magnetic field with an additional parameter modulated harmonic trap potential is studied by using variational method.The equilibrium state equations with or without population difference between the two legs of the bosonic magnetic ladders is obtained analytically.The effects of the interaction,the average strength of harmonic potential and the periodic drive strength on the width of the condensate are discussed.The dependence of the width of the condensate on the tunneling amplitude between the two legs and the population difference is analyzed.It is found that when there is no population difference between the two legs,the external harmonic potential has a great influence on the width of the condensate in the weak interaction.With the strengthening of the interaction,the influence of the external additional parameter modulated harmonic potential on the width of the condensate becomes less and less.The critical condition controlling the stability of the bosonic magnetic ladder system with an additional parameter modulated harmonic trap potential is obtained analytically.The stability of the system can be arrived by regulating the interaction,the average strength of harmonic potential,the tunneling amplitude between the two legs and the periodic drive strength.Finally,a brief summary of these two tasks and prospects in this area are given.