Fast closed-loop optimal control of ultracold atoms in an optical lattice

In the last decade, the implementation of quantum simulators with cold atoms has experienced remarkable expansion. The latest developments in the field have made now possible to experimentally investigate Fermi and Bose ultracold gases in many different setups and optical potentials have given access to the simulation of the ground state physics and of the dynamics of some of the most important lattice models, like Hubbard and spin model. The path towards new experiments of increasing complexity is conditional on the development of more precise experimental techniques, in order to achieve increased control on the system under investigation. It has been shown that it is possible to exploit quantum optimal control to synthesize optimal strategies for correlated quantum many-body dynamics, combining numerical simulations and novel approaches. To this purpose, we present experimental evidence of the successful closed-loop optimization of the dynamics of cold atoms in an optical lattice. We optimize the loading of an ultracold atomic gas minimizing the excitations in an array of one-dimensional tubes (3D-1D crossover) and we perform an optimal crossing of the quantum phase-transition from a Superfluid to a Mott-Insulator in a three-dimensional lattice. In both cases we enhance the experiment performances with respect to those obtained via adiabatic dynamics, effectively speeding up the process.