Research On Bose Atomic Supersolid And Quasicrystal

The manipulation of ultracold atomic gases by laser light provides a perfect platform to ex-plore new phenomena associated with the interaction between light and matter.Among them,many interesting quantum phenomena can be observed by trapping the Bose-Einstein con-densate(BEC)in the optical cavities.For example,Dicke quantum phase transition can be achieved in a linear optical cavity? the formation of supersolid in two crossed cavities and in a ring cavity.The first work of this thesis deals with quantum phase transitions by coupling BEC in two crossed high-finesse cavities.We calculate the ground-state wave function by combining imaginary-time propagation(ITP)with split-step Fourier(SSF)method.We show an intrigu-ing quantum phenomenon on the basis of these two numerical simulations to perfect exper-iments.We present a detailed study of the excitation spectrum in the thermodynamic limit.The spectrum exhibits the mode softening as the pump strength approaches the critical value and appears a Goldstone mode and an amplitude mode,which means the system appears the continuous U(1)symmetry breaking.This is the main sign of the formation of supersolid.In the second part,we explore the quasicrystal.It is a substance that has a long-range ordered but not periodic structure.The quasicrystal with eight-fold rotational symmetry was obtained ex-perimentally by loading the BEC in a system consisting of four optical cavities and irradiating the condensate with laser in the cavities.While we combine ITP and SSF to theoretically ob-tain the octave quasicrystal.This thesis presents systematic theories for exploring the quantum phenomena in different optical cavities.It paves the way for further studying complex systems associated with optical cavities in the future.