Suppression of polaron self-localization by correlations

We investigate self-localization of a polaron in a homogeneous Bose-Einstein condensate in one dimension. This effect, where an impurity is trapped by the deformation that it causes in the surrounding Bose gas, has been first predicted by mean-field calculations, but has not been seen in experiments. We study the system in one dimension, where, according to the mean-field approximation, the self-localization effect is particularly robust and present for arbitrarily weak impurity-boson interactions. We address the question whether self-localization is a real effect by developing a variational method which incorporates impurity-boson correlations nonperturba- tively and solving the resulting inhomogeneous correlated polaron equations. We find that correlations inhibit self-localization except for very strongly repulsive or attractive impurity-boson interactions. Our prediction for the critical interaction strength for self-localization agrees with a sharp drop of the inverse effective mass found in quantum Monte Carlo simulations of polarons in one dimension.