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

Abstract

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 Schrödinger equation and Bloch equations of motion for this system are obtained. We analyze the $$\mathcal{P}\mathcal{T}$$ phase diagram and the dynamical stability of fixed points. The reentrance of $$\mathcal{P}\mathcal{T}$$ -symmetric phase and the reformation of stable fixed points with increasing the nonreciprocity parameter are found. Besides, we uncover a linear selftrapping effect induced by the nonreciprocity. In the nonlinear case, the self-trapping oscillation is enhanced by the nonreciprocity and then collapses in the $$\mathcal{P}\mathcal{T}$$ -broken phase, and can finally be recovered in the reentrant $$\mathcal{P}\mathcal{T}$$ -symmetric phase.

Graphical abstract

Keywords

Bose–Einstein condensate / non-Hermitian physics / nonlinear dynamics / parity–time symmetry

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