Atom cooling by non-adiabatic expansion

TL;DR

This paper demonstrates that non-adiabatic square-root in time expansion of a box is more effective for atom cooling than linear expansion, achieving near-zero energy states without requiring slow processes.

Contribution

It introduces and compares square-root and linear in time expansions, showing the superiority of square-root expansion for quantum atom cooling.

Findings

Square-root expansion asymptotically reaches zero average energy.

Linear expansion leaves residual energy unless infinitely slow.

Square-root expansion maintains cooling despite breakdown of adiabaticity.

Abstract

Motivated by the recent discovery that a reflecting wall moving with a square-root in time trajectory behaves as a universal stopper of classical particles regardless of their initial velocities, we compare linear in time and square-root in time expansions of a box to achieve efficient atom cooling. For the quantum single-atom wavefunctions studied the square-root in time expansion presents important advantages: asymptotically it leads to zero average energy whereas any linear in time (constant box-wall velocity) expansion leaves a non-zero residual energy, except in the limit of an infinitely slow expansion. For finite final times and box lengths we set a number of bounds and cooling principles which again confirm the superior performance of the square-root in time expansion, even more clearly for increasing excitation of the initial state. Breakdown of adiabaticity is generally fatal for cooling with the linear expansion but not so with the square-root expansion.