Quantum Entanglement Manifestation of Transition to Nonlinear Self-trapping for Bose-Einstein Condensates in a Symmetric Double-Well

TL;DR

This paper explores the quantum entanglement aspects of the transition to nonlinear self-trapping in Bose-Einstein condensates within a symmetric double-well, revealing critical behavior, quantum fluctuations effects, and entanglement entropy changes.

Contribution

It provides a detailed analysis of the quantum entanglement manifestation during the phase transition, extending mean-field results to include many-body quantum fluctuations.

Findings

Transition is a continuous phase transition with logarithmic scaling law.

Quantum fluctuations shift the transition point and break the scaling law.

Entanglement entropy peaks at the transition point, indicating quantum criticality.

Abstract

We investigate the nonlinear self-trapping phenomenon of the Bose-Einstein condensates (BEC) in a symmetric double-well, emphasizing on its behind dynamical phase transition. With increasing the nonlinear parameter depicting the interaction between the degenerate atoms the BEC turns to be self-trapped manifesting an asymmetric distribution of the atomic density profile. Essence of this phenomenon is revealed to be a continuous phase transition and underlying critical behavior is studied analytically and found to follow a logarithm scaling-law. We then go beyond the mean field treatment and extend to discuss the effect of the many-body quantum fluctuation on the transition. It is found that the transition point is shifted and the scaling-law is broken. In particular, the quantum phase transition is accompanied by the change of the entanglement entropy which is found to reach maximum at transition point. Behind physics is revealed.