20 years ago, delta kick cooling (DKC) was proposed [1,2] and demonstrated [3,4,5] as a fast technique for cooling quantum gases. Originally conceived using classical arguments, DKC uses a combination of long-time free expansion and conservative forces to reduce temperature at the expense of spatial density, and hence preserves phase-space density. Despite its now common use in ultracold atomic systems, standard DKC is suitable only to the extent that these systems obey approximately classical, non-interacting dynamics. What does DKC look like for a quantum, interacting system? In this talk, I will discuss recent work [6] that introduces an exact approach to DKC for arbitrary scale-invariant dynamics of quantum gases. This modified DKC extends our understanding of ‘kicked cooling’ beyond the limits of free evolution and non-interacting systems. We study the control of quantum gases in time-dependent harmonic traps that can be either repulsive (inverted) or confining. We show that DKC assisted by a repulsive potential outperforms the conventional scheme, and that DKC combined with sudden trap-frequency jumps is a time-optimal protocol, in the limit of instantaneous kicks.

[1] Chu, S., Bjorkholm, J. E., Ashkin, A., Gordon, J. P., & Hollberg, L. W. (1986). Proposal for optically cooling atoms to temperatures of the order of 10^−6 K. *Optics Letters*, *11*(2), 73.

[2] Ammann, H., & Christensen, N. (1997). Delta Kick Cooling: A New Method for Cooling Atoms. *Phys. Rev. Lett.*

[3] Maréchal, E., Guibal, S., Bossennec, J.-L., Barbé, R., Keller, J.-C., & Gorceix, O. (1999). Longitudinal focusing of an atomic cloud using pulsed magnetic forces. *Physical Review A*.

[4] Myrskog, S. H., Fox, J. K., Moon, H. S., Kim, J. B., & Steinberg, A. M. (2000). Modified ``δ-kick cooling’’ using magnetic field gradients. *Phys. Rev. A*.

[5] Aoki, T., Kato, T., Tanami, Y., & Nakamatsu, H. (2006). δ-kick cooling using the Ioffe-Pritchard potential. *Phys. Rev. A*.

[6] Dupays, L., Spierings, D. C., Steinberg, A. M., & del Campo, A. (2021). Exact Delta Kick Cooling, Time-Optimal Control of Scale-Invariant Dynamics, and Shortcuts to Adiabaticity Assisted by Kicks, arXiv:2104.00999.