Real-space dynamics of attractive and repulsive polarons in Bose-Einstein condensates

TL;DR

This paper studies the real-space dynamics of Bose polarons near a Feshbach resonance, revealing long-lived oscillations and impurity motion behaviors through a many-body approach, highlighting differences from Fermi polarons.

Contribution

It introduces a coherent-state variational method to analyze the time evolution of Bose polarons in position space, capturing phenomena not seen in simpler two-body models.

Findings

Long-lived oscillations of Bose polarons on the repulsive side.

Oscillation frequency approximates the two-body bound state energy.

Impurity velocity exhibits periodic slowing and arrest.

Abstract

We investigate the formation of a Bose polaron when a single impurity in a Bose-Einstein condensate is quenched from a non-interacting to an attractively interacting state in the vicinity of a Feshbach resonance. We use a beyond-Fr\"ohlich Hamiltonian to describe both sides of the resonance and a coherent-state variational ansatz to compute the time evolution of boson density profiles in position space. We find that on the repulsive side of the Feshbach resonance, the Bose polaron performs long-lived oscillations, which is surprising given that the two-body problem has only one bound state coupled to a continuum. They arise due to interference between multiply occupied bound states and therefore can be only found with many-body approaches such as the coherent-state ansatz. This is a distinguishing feature of the Bose polaron compared to the Fermi polaron where the bound state can be occupied only once. We derive an implicit equation for the frequency of these oscillations and show that it can be approximated by the energy of the two-body bound state. Finally, we consider an impurity introduced at non-zero velocity and find that, on the repulsive side, it is periodically slowed down or even arrested before speeding up again.