Controlling many-body quantum systems is at the forefront of the development of quantum technologies. To bypass the adiabatic preparation of quantum states, techniques known as shortcuts to adiabaticity (STA) have been developed [1]. In this talk, we will first discuss the extension of the technique of delta-kick cooling to many-body systems verifying scale-invariant dynamics [2]. Delta-kick cooling is commonly used in ultracold atoms to narrow the momentum distribution of atomic clouds. We will demonstrate the link between delta-kick cooling and time-optimal control and present a new type of STA that combines shortcuts and a delta-kick. Afterwards, we will present some progress in the control of gapless many-body quantum systems described by the Tomonaga-Luttinger liquid (TLL). We will provide exact dynamics in the quenched TLL where the interactions are varied in time. Furthermore, we will characterize the residual energy after a finite time quench. To cancel the residual energy, we will propose a STA protocol using counterdiabatic driving [3,4].

 

[1] D Guéry-Odelin, A Ruschhaupt, A Kiely, E Torrontegui, S Martínez-Garaot, JG Muga, Rev. Mod. Phys. 91, 045001 –2019

[2] L. Dupays, D. C. Spierings, A. M. Steinberg, A. del Campo, Phys Rev Research, 2021

[3] L. Dupays, B. Dóra, A. del Campo, arXiv preprint, arXiv:2401.17884, 2024

[4] L. Dupays, A. del Campo, arXiv preprint, arXiv:2404.19013, 2024