Fast Control of Open and Many-Body Quantum Systems

This thesis deals with the fast control of quantum mechanical systems. Fast and reliable control of quantum systems is valuable in the context of quantum technologies, where it helps mitigate the effects of system-environment interactions and preserve coherences. A full range of techniques has been developed for this purpose and are known as shortcuts to adiabaticity. The first part of this thesis aims at extending those techniques to open quantum systems, using the framework of stochastic master equations with two model Hamiltonians: the time-dependent frequency harmonic oscillator and the Jaynes-Cummings model. These shortcuts to adiabaticity in open systems allow us to achieve both squeezing and thermalization in a fast way. In the second part of this thesis, we focus on out-of-equilibrium many-body systems. We first develop a new theoretical formalism for delta kick cooling, a technique to reduce the momentum dispersion of atom clouds, that takes into account interactions between particles. We demonstrate the link between optimal control and delta kick cooling and consider the effects of using a finite kick leading to the breakdown of the original theory. We use the framework of delta kick cooling to control the momentum distribution of the Tonks-Girardeau gas, reversing the phenomenon of dynamical Fermionization with kicks. We also provide a new demonstration of the phenomenon of dynamical Fermionization that does not rely on the stationary phase approximation. In a further chapter, we study the dynamics of the quenched Tomonaga-Luttinger liquid in the Schr\"odinger picture, providing a new method to study quenches in the Tomonaga-Luttinger liquid and the associated residual mean energy. This allows us to determine control protocols to transition from one Tomonaga-Luttinger to another thanks to the modulation of an auxiliary semiclassical sine-Gordon term. We also study the influence of the interaction range on the residual mean energy. Finally, we compute the counterdiabatic driving term in the Tomonaga-Luttinger liquid paving the way for shortcuts to adiabaticity in quantum field theory.