Frictionless atom cooling in harmonic traps: a time-optimal approach

TL;DR

This paper formulates frictionless atom cooling in harmonic traps as a time-optimal control problem, revealing bang-bang solutions and providing practical suboptimal strategies for experimental implementation.

Contribution

It introduces a novel control framework allowing imaginary trap frequencies and derives minimum-time solutions with bang-bang control, plus suboptimal numerical methods for real-world application.

Findings

Minimum cooling time solutions have bang-bang control structure.

Allowing imaginary frequencies enables faster cooling protocols.

Numerical methods produce implementable suboptimal solutions.

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 trasient time intervals during which the trap becomes an expulsive parabolic potential. We show that the minimum time solution has "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.