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Delta kick cooling (DKC) is used to compress the momentum distribution ofultracold quantum matter. It combines expansion dynamics with the use of kickpulses, designed via classical methods, that bring the system to rest. Weintroduce an exact approach to DKC for arbitrary scale-invariant dynamics ofquantum gases, lifting the original restrictions to free evolution andnoninteracting systems, to account for the control of atomic clouds in atime-dependent harmonic trap that can be either repulsive (inverted) orconfining. We show that DKC assisted by a repulsive potential outperforms theconventional scheme, and that sudden trap-frequency quenches combined with DKCare equivalent to time-optimal bang-bang protocols. We further show thatreverse engineering of the scale-invariant dynamics under smooth trap-frequencymodulations can be combined with DKC to introduce a new class of shortcuts toadiabaticity assisted by kicks.

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