The ground state and the tunnelling dynamics of the Bose-Einstein condensate in a tilted shallow trap

Abstract

The ground state and the tunnelling dynamics of the Bose-Einstein condensate (BEC) loaded in a tilted shallow trap is studied analytically and numerically. The stable bound state, the quasi-bound state and the diffusion state are predicted. The thresholds for transition between the different states are obtained and the stability diagram in parameter space is presented. The tunnelling dynamics of the system in different states is revealed. The shape of the potential well and the atomic interaction play important role and have coupled effect on the tunnelling dynamics of the system. Furthermore, the resonant tunnelling phenomenon in the parametrically modulated shallow trap is observed. The results show that when the modulating frequency approaches the dipolar mode of the system, resonant tunnelling occurs and the whole system is unstable. Our results provide a theoretical evidence for studying the tunnelling dynamics of the ultracold atomic system.