Time-Optimal Adiabatic-Like Expansion of Bose-Einstein Condensates

TL;DR

This paper develops a time-optimal control method for rapidly expanding a Bose-Einstein condensate in a harmonic trap, minimizing the expansion time using bang-bang control strategies, with implications for precision atom interferometry.

Contribution

It introduces a novel application of time-optimal control theory to achieve the fastest adiabatic-like expansion of BECs, optimizing experimental procedures.

Findings

Minimum expansion time scales logarithmically with expansion factor

Optimal control involves bang-bang frequency modulation

Potential for improved precision in atom interferometry

Abstract

In this paper we study the fast adiabatic-like expansion of a one-dimensional Bose-Einstein condensate (BEC) confined in a harmonic potential, using the theory of time-optimal control. We find that under reasonable assumptions suggested by the experimental setup, the minimum-time expansion occurs when the frequency of the potential changes in a bang-bang form between the permitted values. We calculate the necessary expansion time and show that it scales logarithmically with large values of the expansion factor. This work is expected to find applications in areas where the efficient manipulations of BEC is of utmost importance. As an example we present the field of atom interferometry with BEC, where the wavelike properties of atoms are used to perform interference experiments that measure with unprecedented precision small shifts induced by phenomena like rotation, acceleration, and gravity gradients.