Mobile dissipative impurities in one-dimensional Bose gases

We study an impurity immersed into a one-dimensional Bose gas with a fluctuating impurity-Bose interaction (i.e. a dissipative „polaron“). We use a mean-field description which takes the deformation of the quasi condensate into account such that quantum fluctuations are small. The stochastic coupling creates a coherent flow of particles towards the impurity, similar to the effect of a local loss. In addition there is an outward flowing incoherent current of particles.  Depending on the amplitude of the noise and the velocity of the impurity a normal or Zeno-like quasi stationary state emerges. Above a critical value of the velocity there is a continuous emission of solitons such that no stationary state forms even for a subsonic impurity. In the case of two impurities, we find evidence for a dissipation-mediated long-range interaction between the impurities for weak noise, while strong noise results, similar as a moving impurity, in a constant creation of solitons.