Quantum simulators: the Anderson transition with cold atoms

Jean Claude Garreau

Jean Claude Garreau

The Anderson model is a paradigm for quantum disordered physical systems. Originally conceived in a condensed matter context, it is however difficult to study experimentally in solids. The quantum kicked rotor which has also a paradigmatic status for classical and quantum Hamiltonian chaotic systems, can be easily realized using laser-cooled atoms in a standing wave. Somewhat surprisingly, there is a mathematical mapping between these two systems, and the latter can be used as a "quantum simulator" for the former. In this talk, I will describe a series of experiments using the atomic kicked rotor allowing a rather complete characterization of the Anderson physics, and in particular a precise determination of the critical exponent of the Anderson metal-insulator transition.

Xingbo Wei, Xuewei Zuo

We investigate the localization transition in a one-dimensional extended Aubry–André–Harper (AAH) model, emphasizing its implementation as a quantum simulator in ultracold atomic optical lattices. In the single-particle case, quasi-periodic hopping modulation allows the localization transition point to be clearly observed even for small system sizes. By driving the system into strongly Anderson localized states immediately after the transition, we observe a sharp many-body localization (MBL) transition upon introducing interactions, with the MBL transition point closely approaching that of Anderson localization. To demonstrate the effects of interactions, we map out a global phase diagram and find that critical states in this model are easily thermalized. Contrary to previous studies where enhanced interactions significantly promoted thermalization, we find that increasing interactions does not notably shift the MBL transition point. Importantly, our setup offers a practical and experimentally accessible platform for studying sharp MBL transitions using ultracold atoms in optical lattices, bridging MBL physics with advances in quantum optics and cold-atom technologies.

Hui Zhai

Jean Claude Garreau

Jean Claude Garreau

Quantum simulation is one of the most active trends in ultracold-atom physics. A quantum simulator is a system that mimics the dynamics of another system; the advantage being that the quantum simulator is simpler than the original, either from the experimental or the theoretical point of view (or both).The Anderson model is a paradigm for quantum disorder, originally introduced in the helm of solid-state physics; however, quantum solid-state disordered systems are very difficult to study experimentally, and even numerically (except in the one-dimensional case). The kicked rotor is a paradigm for classical and quantum Hamiltonian chaos, essentially because it is very easy to simulate it in a computer. Its quantum realization with ultracold atoms is also relatively simple, and is a “clean” (e.g. from decoherence) and controllable system. Amazingly, the quantum kicked rotor can be mathematically mapped onto the Anderson model. It is thus a quite subtle quantum simulator of the physics of disordered systems. In this talk I will describe a series of experiments we have performed in Lille taking advantage of the correspondence between disordered condensed matter systems and the atomic kicked rotor to investigate experimentally in great detail the Anderson metal-insulator transition. I will discuss the new possibilities opened by evolutions of this system, in particular by introducing nonlinearity via atom-atom interactions.