  The field of quantum simulation, which aims at using a tunable quantum system
to simulate another, has been developing fast in the past years as an
alternative to the all-purpose quantum computer. In particular, the use of
temporal driving has attracted a huge interest recently as it was shown that
certain fast drivings can create new topological effects, while a strong
driving leads to e.g. Anderson localization physics. In this work, we focus on
the intermediate regime to observe a quantum chaos transport mechanism called
chaos-assisted tunneling which provides new possibilities of control for
quantum simulation. Indeed, this regime generates a rich classical phase space
where stable trajectories form islands surrounded by a large sea of unstable
chaotic orbits. This mimics an effective superlattice for the quantum states
localized in the regular islands, with new controllable tunneling properties.
Besides the standard textbook tunneling through a potential barrier,
chaos-assisted tunneling corresponds to a much richer tunneling process where
the coupling between quantum states located in neighboring regular islands is
mediated by other states spread over the chaotic sea. This process induces
sharp resonances where the tunneling rate varies by orders of magnitude over a
short range of parameters. We experimentally demonstrate and characterize these
resonances for the first time in a quantum system. This opens the way to new
kinds of quantum simulations with long-range transport and new types of control
of quantum systems through complexity.
