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 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 selftrapping 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.

Nonlinear perturbation of a high-order exceptional point: Skin discrete breathers and the hierarchical power-law scaling

“…[37][38][39] However, DBs have less direct communications with the non-Hermiticity. Some theoretical works [40][41][42][43][44][45][46][47] have already touched upon the crossing scenarios of nonlinearity and non-Hermiticity. For example, an end breather oscillating at one boundary is proposed in a non-Hermitian Su-Schrieffer-Heeger-like lattice with saturable nonlinearity due to the interplay of non-Hermitian skin effect and the topological end state.…”

“…[42] In one-dimensional discrete nonlinear Schrödinger equations with nonreciprocal hopping, fractal bands are numerically figured out, [43] and several different trapped skin states are formed in quench dynamics. [46] Nonlinear effects on EPs [47] or nonlinear EPs [44,45] are also discussed in different non-Hermitian nonlinear models. In experiments, topological insulator lasers [48,49] and the nonlinear Thouless pumping [50] are realized by utilizing the merits of chiral edge states of Hermitian topological systems and self-trapping of nonlinearity.…”