Phase Transitions And Dynamics Of Biased Bosonic Ladders With Magnetic Flux

In recent years,the realizations of the artificial gauge fields and optical lat-tices provide an ideal playground to explore intriguing phenomena in condensed physics.Ladders as simple models exhibiting behavior of many artificially man-ufactured structures and naturally found compounds attract growing interest in strongly correlated electron system.The experimental realization and theoreti-cal investigation of bosonic ladder system have greatly promoted the researchs in quantum Hall effects,topological physics and Hofstadter butterfly phenomena.Recently,the experiment realized the quantum phase transition from the Vortex phase to the Meissner phase in the ladder system,which also open a new path to implement spin-orbit(SO)coupling in one dimensional quantum gases.The adding Zeeman field leads to rich phase transition processes in spin-orbit-coupled Bose-Einstein condensate.However,it is still an opening subject to explore the ground state properties and dynamical features in the ladder system with the similar Zeeman field.In this paper,we investigate the quantum phase transi-tions and dynamics of biased bosonic ladders subject to the magnetic field.The paper is organized as follows.In the first chapter,a brief introduction to the bosonic ladders is made,including the realization of the artificial gauge fields and optical lattices in this system.Then we introduce some backgrounds and present research situations of the bosonic ladders subject to a magnetic field.In the second chapter,the ground states and the dynamics of a biased two-leg Bose-Hubbard flux ladder in the presence of a gravitational field are discussed.In analogy to the Spin-Orbit coupling system with Zeeman field,the adding controlled energy bias between the two legs of the ladder can realize a biased bosonic ladder,which has been shown to possess the essence of such SO coupling system.In the absence of the gravitational field,the ground states and the critical condition of phase transition are obtained analytically.We identify the Meissner phase,Vortex phase,and interestingly,two new Plane Wave phases,that break both Z₂and time-reversal symmetry,characterized by the imbalance particle density distribution,asymmetry double well energy band structure in Plane Wave I(PWI)phase and asymmetry single well energy band structure in Plane Wave II(PWII)phase,respectively.In the presence of a longitudinal dc gravitational field,rich chiral Bloch oscillation and Landau-Zener tunneling are predicted theoretically and confirmed numerically.The characteristics of the chiral Bloch oscillation can distinguish the novel phases intuitively.In the third chapter,by the variational method and the Gross-Pitaevskii approach,we first achieve the ground states and phase transition conditions of the biased interacting bosonic ladder system with magnetic flux.Rich phases are revealed,including the Meissner phase,Vortex phase,BLP,and interestingly,two new Plane Wave phases,that break both Z₂and time-reversal symmetry,and Moving Biased Vortex phase(MBVP),which also breaks Z₂reflection sym-metry and characterized by the moving vortex with imbalance particle density distribution.Remarkably,the energy bias results in the occurrence of a tricritical point at the phase boundary of these phases in the magnetic flux,interaction and rung-to-leg coupling ratio plane.Finally,a brief summary of these two tasks and prospects in this area are given.