Mobile-impurity dynamics in a non-Hermitian Stark-localised bath

Abstract

We investigate the dynamics of a clean mobile impurity coupled to a bath subjected to a linear Stark potential as well as asymmetric hopping in one dimension. The impurity mediates resonant tunnelling in the bath whenever the interaction strength matches the Stark potential and leads to loss in the memory of the initial state of the bath particles. The non-Hermitian asymmetry does not shift these resonances but reshapes them directionally, and it destroys the bath's Stark-induced memory through the non-Hermitian skin effect. On the other hand, we find that the impurity is localised only within an intermediate range of Stark potential. At very weak tilt strengths the bath offers no potential to trap the impurity, while at strong tilt the bath freezes into a nearly periodic charge density wave that pushes the impurity towards partial localisation. Counterintuitively, the impurity localises in the intermediate regime where the bath's initial-state memory is strongly suppressed, yet a spatially inhomogeneous density profile persists. The interaction amplifies these density fluctuations, dressing the impurity with an effective disordered potential that traps it. Since the skin effect degrades this intermediate density distribution, the impurity localisation window shifts toward stronger tilt in the non-Hermitian regime.