Effect of spin-orbit coupling on tunnelling escape of Bose-Einstein condensate.

We theoretically investigate quantum tunnelling escape of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) from a trapping well. The condensate is initially prepared in a quasi-one-dimensional harmonic trap. Depending on the system parameters, the ground state can fall in different phases --- single minimum, separated or stripe. Then, suddenly the trapping well is opened at one side. The subsequent dynamics of the condensate is studied by solving nonlinear Schr\"{o}dinger equations. We found that the diverse phases will greatly change the tunneling escape behavior of SO coupled BECs. In single minimum and separated phases, the condensate escapes the trapping well continuously, while in stripe phase it escapes the well as an array of pulses. We also found that SO coupling has a suppressing effect on the tunnelling escape of atoms. Especially, for BECs without inter-atom interaction, the tunnelling escape can be almost completely eliminated when the system is tuned near the transition point between single minimum and stripe phase. Our work thus suggests that SO coupling may be a useful tool to control the tunnelling dynamic of BECs, and potentially be applied in realization of atom lasers and matter wave switches.