Occupation Statistics of a BEC for a Driven Landau-Zener Crossing

TL;DR

This paper investigates the occupation statistics of a Bose-Einstein condensate in a double-well trap during a Landau-Zener crossing, analyzing how interactions and sweep rates influence the system's dynamical regimes beyond mean-field approximations.

Contribution

It introduces a detailed analysis of the BEC dynamics during a Landau-Zener crossing, including regimes beyond mean-field theory and a semiclassical interpretation.

Findings

Identification of three dynamical regimes: adiabatic, diabatic, and sudden.

Analysis of occupation statistics depending on interaction strength and sweep rate.

Extension beyond mean-field theory with semiclassical insights.

Abstract

We consider an atomic Bose-Einstein condensate (BEC) loaded in a biased double-well trap with tunneling rate $K$ and inter-atomic interaction $U$. The BEC is prepared such that all $N$ atoms are in the left well. We drive the system by sweeping the potential difference $\epsilon$ between the two wells. Depending on the interaction $u=NU/K$, and the sweep rate $\dot{\epsilon}$, we distinguish three dynamical regimes: adiabatic, diabatic, and sudden, and consider the occupation statistics of the final state. The analysis goes beyond mean-field theory and is complemented by a semiclassical picture.