  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.
