Quantum Monte-Carlo simulation of polaron tunneling

Polaron tunneling is a prominent example of a task with the different energy scales, for which using the standard quantum Monte-Carlo methods faces a slow-down problem. We construct a path-integral quantum Monte-Carlo method which is free from this issue and apply it to study an impurity interacting with a one-dimensional Bose-Einstein condensate and simultaneously trapped in an external double-well potential. Our scheme works for an arbitrary coupling between the particle and condensate and, at the same time, allows for an account of tunneling effects. We observe two distinct quasi-particle peaks associated, respectively, with the phonon-assisted tunneling and the self-trapping of the impurity, which are in a crossover regime for the system modelled. While increasing the coupling strength in the Frohlich-Bogoliubov model, we observe changes in the peak's weights and their spectral positions (or, equally, effective masses of the quasi-particles). Possible experimental realizations with cold atoms are discussed.