The Role of Singular Control in Frictionless Atom Cooling in a Harmonic Trapping Potential
Provides a theoretical control strategy for minimizing transient energy in atom cooling, relevant to quantum computing and thermodynamics, but the results are incremental.
The authors show that frictionless cooling of atoms in a harmonic trap with unbounded control is achieved by singular control, which also solves a dual time-minimal problem. They briefly examine bounded control modifications.
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.