Dynamics Of Bose Condensed Atoms In A Time-periodically Driven PT Symmetric Double-well Potential

Parity-time(PT) symmetry, the invariance under parity-time reflection, is an important concept in quantum physics. Attribute their robust quantum coherence and hight controllability, ultra Bose condensed atomic gases provide a new platform for exploring quantum property and dynamics of PT-symmetric open many-body quantum system. Based upon non-Hermitian Hamiltonian described open quantum system, we investigate many-body quantum dynamics and quantum manipulation of Bose condensed atoms confined in a time-periodically driven PT symmetric double-well potential in this thesis.In the first chapter, we mainly introduce the concept of PT symmetry, review the theory of Bose-Einstein condensation, and discuss PT symmetric non-Hermitian two mode Bose-Hubbard Hamiltonian.In Chapter 2, we investigate the manipulation of PT symmetry and the effect of PT symmetry on quantum tunneling dynamics for a periodically driven PT-symmetric non-Hermitian two-level system. Applying both analytical and numerical approaches,we explore how to manipulate PT symmetry of the system by tuning the driving amplitude and frequency. By analyzing the relationship of the PT symmetry and quantum tunneling dynamics, it is found that the quantum tunneling between two levels can be suppressed in a wide range of parameters in comparison with the Hermitian case,which is caused by the PT-symmetry-breaking. Our results provide a promising approach for manipulating the PT symmetry by applying a periodic driving field.In Chapter 3, we investigate how to manipulate the PT symmetry of open many-body quantum system via applying a periodic driving field. For a periodically driven PT-symmetric non-Hermitian Bose-Hubbard dimmer, the Floquet energy spectrum and phase diagram of the PT symmetry are analytically and numerically given.The parametric dependence of spontaneous PT-symmetry-breaking transition is analyzed. The region of unbroken PT symmetry sensitively depends on the interaction strength between atoms as well as driving amplitude and frequency. Therefore, one can manipulate the PT symmetry of open many-body quantum system by tuning the interatomic interaction or the driving parameter.In Chapter 4, we briefly summarize our results and present some expectations in this field.Throughout the paper we will explore how to manipulate the PT symmetry of PT-symmetric many-body quantum system by applying the external driving field. Our main works are involved in chapters 2 and 3.