The Anderson metal-insulator transition in a quantum-chaotic system of laser-cooled atoms

W. W. Cheng, Z.J. Zhang, Longyan Gong +1 more

Jean Claude Garreau

W. W. Cheng, Jiaxin Li, Chuan-Jia Shan +2 more

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.

Julien Chabé, Gabriel Lemarié, Benoît Grémaud +3 more

We realize experimentally an atom-optics quantum-chaotic system, the quasiperiodic kicked rotor, which is equivalent to a 3D disordered system that allows us to demonstrate the Anderson metal-insulator transition. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to extract both the critical parameters and the critical exponent of the transition, the latter being in good agreement with the value obtained in numerical simulations of the 3D Anderson model.

Gabriel Lemarié, Julien Chabé, Pascal Szriftgiser +3 more

Using a cold atomic gas exposed to laser pulses---a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies---we study experimentally and theoretically the Anderson metal-insulator transition in three dimensions. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to unambiguously demonstrate the existence of a quantum phase transition and to measure its critical exponents. By taking proper account of systematic corrections to one-parameter scaling, we show the universality of the critical exponent $\ensuremath{\nu}=1.59\ifmmode\pm\else\textpm\fi{}0.01$, which is found to be equal to the one previously computed for the Anderson model.