The Role of Singular Control in Frictionless Atom Cooling in a Harmonic Trapping Potential

Details The Role of Singular Control in Frictionless Atom Cooling in a Harmonic Trapping Potential The Role of Singular Control in Frictionless Atom Cooling in a Harmonic Trapping Potential

2011-03-08

arxiv.org/abs/1103.1665v1

Mathematics

Optimization and Control

Scientific paper

In this article we study the frictionless cooling of atoms trapped in a harmonic potential, while minimizing the transient energy of the system. We show that in the case of unbounded control, this goal is achieved by a singular control, which is also the time-minimal solution for a "dual" problem, where the energy is held fixed. In addition, we examine briefly how the solution is modified when there are bounds on the control. The results presented here have a broad range of applications, from the cooling of a Bose-Einstein condensate confined in a harmonic trap to adiabatic quantum computing and finite time thermodynamic processes.

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