Frictionless atom cooling in harmonic traps: A time-optimal approach
Dionisis StefanatosDepartment of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USAJustin RuthsDepartment of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USAJr-Shin LiDepartment of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USA
2010en
ABI
Abstract
In this article we formulate frictionless atom cooling in harmonic traps as a time-optimal control problem, permitting imaginary values of the trap frequency for transient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has a ``bang-bang'' form, where the frequency jumps suddenly at certain instants and then remains constant, and calculate estimates of the minimum cooling time for various numbers of such jumps. A numerical optimization method based on pseudospectral approximations is used to obtain suboptimal realistic solutions without discontinuities, which may be implemented experimentally.
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