Impurity in a Bose-Einstein condensate in a double well

TL;DR

This paper investigates the effects of a single impurity on a Bose-Einstein condensate in a double well, revealing bifurcations, spontaneous imbalance, and entanglement phenomena through mean-field and many-body analyses.

Contribution

It introduces a detailed comparison of mean-field and many-body properties of impurity-laden condensates, highlighting bifurcations and entanglement at critical interaction strengths.

Findings

Bifurcations occur as boson-impurity interaction varies.

Spontaneous particle imbalance emerges at critical interaction.

Enhanced coherence observed at bifurcation points.

Abstract

We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.