Variational approach to the two-dimensional Bose polaron

TL;DR

This paper develops a variational method to study the two-dimensional Bose polaron, revealing two quasiparticle branches and emphasizing the importance of three excitations for accurate energy predictions, with results aligning with quantum Monte Carlo data.

Contribution

It introduces a variational ansatz with up to three Bogoliubov excitations for the 2D Bose polaron, capturing strong attraction regimes and comparing well with existing quantum Monte Carlo results.

Findings

Identification of attractive and repulsive polaron branches.

Three excitations are essential for accurate attractive polaron energies.

Significant differences in effective mass and residue between interacting and non-interacting BECs.

Abstract

An impurity particle interacting with a Bose-Einstein condensate (BEC) leads to the formation of a quasiparticle known as the Bose polaron. We investigate the properties of the two-dimensional Bose polaron, applying a variational ansatz that contains up to three Bogoliubov excitations of the BEC. Similar to its three-dimensional counterpart, we observe the existence of two quasiparticle branches, namely the attractive and the repulsive polarons, at different coupling strengths. We find that their energies agree well with recent quantum Monte Carlo calculations. In particular, we observe that the inclusion of three excitations is crucial to capture the attractive polaron energy towards the regime of strong attraction, where the quasiparticle properties are dominated by few-body correlations. We also calculate the attractive polaron effective mass and residue, where we find significant differences between considering a weakly interacting Bose medium and taking the non-interacting limit, signalling enhanced impurity dressing by excitations in the latter case. By contrast, the spectral weight of the metastable repulsive polaron is largely insensitive to the interactions in the BEC and the number of Bogoliubov excitations. Our model may be experimentally realized in dilute atomic vapors and atomically thin semiconductors.