Quantum tunnelling of a weakly open Bose–Einstein condensate in a double well under periodic driving

We analyse the dynamics of a weakly open Bose–Einstein condensate (BEC) with attractive atomic interactions in a double-well potential under periodic driving. We find that the inclusion of weakly dissipative effects can dramatically modify the quantum tunnelling of the periodically driven BEC, and some new interesting dynamical properties arise, including a pitchfork bifurcation that leads to two stable nonsymmetric states by adjusting the dissipative parameters. The numerical results based on the approximate two-mode model are also analysed.