Quantum dynamics of impurities in a Bose-Einstein condensate

TL;DR

This paper investigates the quantum dynamics of two impurities in a trapped quasi-one-dimensional Bose-Einstein condensate, analyzing how different interaction strengths influence impurity behavior and the generation of excitations.

Contribution

It provides a detailed analysis of impurity dynamics and excitation phenomena in BECs under varying interaction regimes, highlighting the role of quench dynamics.

Findings

Impurities oscillate or become trapped depending on interaction strength.

Strong interactions suppress impurity motion and affect excitation generation.

Impurity-BEC interactions influence phonon, shock wave, and soliton formation.

Abstract

We study the quantum dynamics of the two impurities in a trapped quasi-one-dimensional Bose-Einstein condensate (BEC). We explore the effect of impurity-BEC and impurity-impurity interaction strengths on the dynamics of impurities inside the Bose-Einstein condensate. By studying the auto-correlation function of impurities and the BEC, we analyze and quantify the trapping of impurities inside the BEC. We find out that for the small value of inter-species coupling strength the BEC starts to oscillate inside the trap. For mild coupling strengths, attractive and repulsive impurities are captured after a few cycles of oscillation inside the BEC. In the strong interaction strength regime, the to-and-fro motion of impurities is suppressed quite fast. Our conclusion indicates that quench dynamics can be a tool for studying impurity BEC interactions or impurity-impurity interactions. Our analysis shows that the generation of phonon, shock waves, soliton trains, and self-trapping is strongly dependent on the impurity-BEC coupling coefficient.