Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential

We investigate the mean-field energy spectrum and dynamics in a Bose-Einstein condensate in a double-well potential with non-Hermiticity from the nonreciprocal hopping, and show that the interplay of nonreciprocity and nonlinearity leads to exotic properties. Under the two-mode and mean-field approximations, the nonreciprocal generalization of the nonlinear Schr\"{o}dinger equation and Bloch equations of motion for this system are obtained. We analyze the PT phase diagram and the dynamical stability of fixed points. The reentrance of PT-symmetric phase and the reformation of stable fixed points with increasing the nonreciprocity parameter are found. Besides, we uncover a linear self-trapping effect induced by the nonreciprocity. In the nonlinear case, the self-trapping oscillation is enhanced by the nonreciprocity and then collapses in the PT-broken phase, and can finally be recovered in the reentrant PT-symmetric phase.