Variational approach to the ground state of an impurity in Bose-Einstein condensate

TL;DR

This paper uses a variational approach with path integrals to study the self-localization of an impurity in a Bose-Einstein condensate, recovering previous results and exploring strong coupling effects.

Contribution

It introduces a variational method based on Feynman's approach to analyze impurity localization in BECs, extending understanding beyond Gross-Pitaevskii predictions.

Findings

Self-localization effect confirmed within variational framework

Correlation functions computed for different coupling regimes

Strong coupling regime with negative ground state energy identified

Abstract

In this paper we consider the effect of self-localization of a quantum impurity in Bose-Einstein condensate. Space correlation function of the impurity is evaluated with the help of the imaginary-time path integral approach. Employing the Feynman's variational method we calculate the impurity correlation function as well as the energy of the system associated with the impurity. The effect of self-localization predicted before within Gross-Pitaevskii approach is recovered by our treatment. The strong coupling regime with negative ground state energy is reached by variational method, and corresponding correlation function is calculated.