Exact Delta Kick Cooling, Time-Optimal Control of Scale-Invariant Dynamics, and Shortcuts to Adiabaticity Assisted by Kicks

TL;DR

This paper develops an exact, versatile approach to delta kick cooling for quantum gases, enabling faster, optimized control of atomic clouds in various trap configurations, and introduces new shortcuts to adiabaticity.

Contribution

It extends delta kick cooling to arbitrary scale-invariant dynamics, including repulsive traps, and links sudden quenches to time-optimal protocols, also proposing new shortcuts to adiabaticity.

Findings

Repulsive potentials improve cooling efficiency.

Sudden trap-frequency quenches are time-optimal.

Smooth modulations combined with kicks create new shortcuts.

Abstract

Delta kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring the system to rest. We introduce an exact approach to DKC for arbitrary scale-invariant dynamics of quantum gases, lifting the original restrictions to free evolution and noninteracting systems, to account for the control of atomic clouds in a time-dependent harmonic trap that can be either repulsive (inverted) or confining. We show that DKC assisted by a repulsive potential outperforms the conventional scheme, and that sudden trap-frequency quenches combined with DKC are equivalent to time-optimal bang-bang protocols. We further show that reverse engineering of the scale-invariant dynamics under smooth trap-frequency modulations can be combined with DKC to introduce a new class of shortcuts to adiabaticity assisted by kicks.