Quantum corrections to the dynamics of the Bose-Einstein condensate in a double-well potential

TL;DR

This paper develops a quantum-corrected model for the dynamics of a Bose-Einstein condensate in a double-well potential, extending mean-field theory by including higher-order interaction effects for more accurate descriptions.

Contribution

It introduces a fully quantized approach with new correction terms accounting for interactions beyond the on-site interaction, enhancing the understanding of BEC dynamics.

Findings

Quantum corrections significantly affect BEC dynamics in double-well potentials.

New interaction terms improve the accuracy of the two-mode BEC model.

The approach extends mean-field results to include higher-order effects.

Abstract

The dynamics of the Bose-Einstein condensate (BEC) in a double-well potential is of- ten investigated under the mean-field theory (MFT). This works successfully for large particle numbers with dynamical stability. But for dynamical instabilities, quantum cor- rections to the MFT becomes important [Phys.Rev.A 64, 013605(2001)]. Recently the adiabatic dynamics of the double-well BEC is investigated under the MFT in terms of a dark variable [Phys.Rev.A 81, 043621(2010)], which generalizes the adiabatic passage techniques in quantum optics to the nonlinear matter-wave case. We give a fully quan- tized version of it using second-quantization and introduce new correction terms from higher order interactions beyond the on-site interaction, which are interactions between the tunneling particle and the particle in the well and interactions between the tunneling particles. If only the on-site interaction is considered, this reduces to the usual two-mode BEC.