Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

TL;DR

This paper develops an optimal control approach to efficiently transfer Bose-Einstein Condensates in a double-well potential, combining Galerkin truncation, CRAB method, and genetic algorithms to optimize the process.

Contribution

It introduces a reduced dynamical system using three modes for controlling BEC transfer, integrating the CRAB method with genetic algorithms for optimization.

Findings

Three-mode Galerkin truncation effectively controls BEC dynamics.

The CRAB method combined with differential evolution optimizes control potentials.

Refinement possible by including more modes in the Galerkin reduction.

Abstract

We pose the problem of transferring a Bose-Einstein Condensate (BEC) from one side of a double-well potential to the other as an optimal control problem for determining the time-dependent form of the potential. We derive a reduced dynamical system using a Galerkin truncation onto a finite set of eigenfunctions and find that including three modes suffices to effectively control the full dynamics, described by the Gross-Pitaevskii model of BEC. The functional form of the control is reduced to finite dimensions by using another Galerkin-type method called the chopped random basis (CRAB) method, which is then optimized by a genetic algorithm called differential evolution (DE). Finally, we discuss the extent to which the reduction-based optimal control strategy can be refined by means of including more modes in the Galerkin reduction.