Adiabatic Splitting, Transport, and Self-Trapping of a Bose-Einstein Condensate in a Double-Well Potential

TL;DR

This paper explores adiabatic control of a Bose-Einstein condensate in a double-well potential, introducing a dark variable approach to achieve splitting, transport, and self-trapping, while analyzing non-linear eigenstates and stability.

Contribution

It extends adiabatic passage techniques to non-linear matter waves, providing a new framework for controlling BEC dynamics in double-well systems.

Findings

Successful adiabatic splitting and transport of BECs demonstrated.

Identification of conditions for adiabatic self-trapping states.

Analysis of non-linear eigenstates and their impact on adiabaticity.

Abstract

We show that the adiabatic dynamics of a Bose-Einstein condensate (BEC) in a double well potential can be described in terms of a dark variable resulting from the combination of the population imbalance and the spatial atomic coherence between the two wells. By means of this dark variable, we extend, to the non-linear matter wave case, the recent proposal by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)] on adiabatic passage techniques to coherently control the population of two internal levels of an atom/molecule. We investigate the conditions to adiabatically split or transport a BEC as well as to prepare an adiabatic self trapping state by the optimal delayed temporal variation of the tunneling rate via either the energy bias between the two wells or the BEC non-linearity. The emergence of non-linear eigenstates and unstable stationary solutions of the system as well as their role in the breaking down of the adiabatic dynamics is investigated in detail.