The Research On Dynamics Of Spin-orbit Coupling Bose-Josephson Junction In Optical Cavity

The coupled of Bose-Einstein condensates(BEC)with highly fine single-mode optical cavities not only expands the study of quantum dynamics of existing cavities,but also provides an effective platform for simulating tunneling dynamics and self-trapping behavior of Josephson junctions with ultra-cold atoms.The atomic cavity system can used in quantum information processing,quantum communication,quantum nondestructive measurement and other fields.Because of the atomic motion of the condensate in the double well are very similar the electron in the solid crystal,and the BEC has superfluidity and macroscopic properties.In this paper,we study simulate the superconducting Josephson junction using BEC modulation in the optical cavity.In addition,We apply the method of phase diagrams to study the mean-field dynamics of a spin-orbit coupled(SOC)Boson Josephson junction(BJJ).First,we consider the existence of equal-Rasba-Dresselhaus SOC in the BJJ.By means of the Heisenberg's equation and two-mode approximation,we derive the mean field dynamic equation of the SOC BJJ in the optical cavity and the Hamiltonian of BJJ.Secondly,according to the different motion modes of spin BJJ 0-phase and ?-phase,we draw the phase diagram of spin BJJ.We not only give the phase diagram between the cavity field parameters,but also give the phase diagram about the SOC and the spin-atom interaction energy.We also find that the SOC BJJ in an optical cavity has four more combinations of 0-phase and ?-phase motion modes than the bare junction.Meanwhile,the strength of SOC,the energy of spinweak atom interaction,the detuning and the drive of cavity field can increase the number of stable point of the energy and enhance the Josephson effect of atoms.While the increase of cavity field dissipation will decrease the number of stable point of the energy.Finally,we can judge the spin atoms are in Josephson effect or self-trapping state from the evolution diagram of the photon number in the cavity.When the spin atoms are in Josephson effect,the total spin atom current and the net spin atom current in the cavity will be zero or twice the spin(up or down)atoms current density with the selection of the initial state.Furthermore,the quantum chaotic behavior of spin atoms under Josephson tunneling is explored in this paper.