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

TL;DR

This paper investigates how singular control strategies enable frictionless atom cooling in harmonic traps, optimizing energy minimization and time efficiency, with implications for quantum computing and thermodynamics.

Contribution

It demonstrates the use of singular control for optimal frictionless atom cooling and explores the effects of control bounds on the solution.

Findings

Singular control achieves minimal transient energy in atom cooling.

Unbounded control leads to time-minimal solutions.

Control bounds modify the cooling strategy.

Abstract

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.