COCOA

The project brings together experimentalists and theoreticians from Toulouse (LCAR UMR 5589, LPT UMR5152) and Orsay (LPTMS 8626). We propose a new approach to cold atom experiments, where a controlled complexity renders a single system very versatile. The complexity will be built progressively in the course of the project upon the interplay between different physical phenomena: tunnel effect, chaos, quantum localization and interaction effects. It will allow us not only to investigate many new regimes of fundamental physics (from disordered to strongly correlated systems) but also to create innovative tools to manipulate cold atoms. To this end, we will focus on a system composed of ultra-cold atoms trapped in a one-dimensional optical lattice, whose amplitude and phase are engineered in time. By time-modulating the lattice amplitude, the system will be driven periodically in a non-perturbative way, leading to the dressing of the lattice by chaos: regular islands will be embedded in a chaotic sea. The central physical effect that will be used is chaos-assisted tunneling (CAT) occurring in such system. CAT presents resonances allowing to tune over orders of magnitude the tunneling rate between two regular islands, over a short range of parameter (e.g. the frequency of lattice modulation). We will first demonstrate these strong variations and fully characterize the distribution of resonances, which have not been observed so far with cold atoms. Then we will build and control step by step the complexity by adding quantum localization effects and atom-atom interactions. These new ingredients have never been considered in the context of CAT. Their inclusion constitutes a theoretical and experimental challenge. The transport between regular islands can be tuned in our system from diffusive to localized, leading to new regimes of tunneling which will be characterized by their tunneling rate distributions. In particular we want to use CAT as a clear signature of multifractality, an intriguing characteristic of the localization transition which remains elusive experimentally. We also want to build a fundamental understanding of the effects of interactions on CAT. We will start from the non-linear regime associated with large number of atoms per lattice site to revisit e.g. the Josephson effect in the chaotic regime. We will then access the strongly-correlated regime by using the experimental apparatus with a 3D lattice. Based on these fundamental outcomes, we will develop new techniques to manipulate cold atoms in optical lattices. The dressing by chaos offers indeed fascinating possibilities for long-range hoppings in dynamical lattices. In the presence of interactions, CAT enables also to tune the ratio between hopping amplitude and interaction strength through resonances reminiscent of Feshbach resonances. These new tools, as they rely on the universal physics of CAT, are independent of the atomic species. They can also be easily transposed in 2D and 3D. They will allow controlling complex cold atoms systems in an unprecedented manner as well as reaching physics models and regimes that are currently inaccessible. The three partners include a cold atom experimental team, a theoretical team specialist of Anderson localization and working at the interface with experiments and a theoretical team expert in CAT and many-body effects. The partners bring key-skills to the project based on their complementary domains of expertise.