  The quantum kicked rotor is a paradigmatic model system in quantum physics.
As a driven quantum system, it is used to study the transition from the
classical to the quantum world and to elucidate the emergence of chaos and
diffusion. In contrast to its classical counterpart, it features dynamical
localization, specifically Anderson localization in momentum space. The
interacting many-body kicked rotor is believed to break localization, as recent
experiments suggest. Here, we present evidence for many-body dynamical
localization for the Lieb-Liniger version of the many-body quantum kicked
rotor. After some initial evolution, the momentum distribution of interacting
quantum-degenerate bosonic atoms in one-dimensional geometry, kicked hundreds
of times by means of a pulsed sinusoidal potential, stops spreading. We
quantify the arrested evolution by analysing the energy and the information
entropy of the system as the interaction strength is tuned. In the limiting
cases of vanishing and strong interactions, the first-order correlation
function exhibits a very different decay behavior. Our results shed light on
the boundary between the classical, chaotic world and the realm of quantum
physics.
