Title :
Time-optimal adiabatic-like expansion of Bose-Einstein condensates
Author :
Stefanatos, Dionisis ; Shin Li
Author_Institution :
Dept. of Electr. & Syst. Eng., Washington Univ., St. Louis, MO, USA
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.
Keywords :
Bose-Einstein condensation; bang-bang control; BEC; Bose-Einstein condensates; adiabatic-like expansion; atom interferometry; atom wavelike properties; bang-bang form; expansion factor; expansion time; gravity gradients; harmonic potential; minimum-time expansion; time-optimal adiabatic-like expansion; time-optimal control; Atomic measurements; Equations; Harmonic analysis; Optimal control; Switches; Trajectory; Vectors;
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2012.6426290