We realize experimentally an atom-optics quantum chaotic system, the quasiperiodic kicked rotor, which is equivalent to a 3D disordered system, that allow us to demonstrate the Anderson metalinsulator transition. Sensitive measurements of the atomic wavefunction dynamics and the use of finite-size scaling techniques make it possible to extract both the critical parameters and the critical exponent of the transition, which is in good agreement with the value obtained in numerical simulations of the 3D Anderson model. The metal-insulator Anderson transition plays a central role in the study of quantum disordered systems. An insulator is associated with localized states of the system, while a metal generally displays diffusive transport associated with delocalized states. The Anderson model [1] describes such a metal-insulator transition, due to quantum interference effects driven by the amount of disorder in the system. Starting from the "tight-binding" description of an electron in a crystal lattice, Anderson postulated in 1958 that the dominant effect of impurities in the lattice is to randomize the diagonal, on-site, term of the Hamiltonian, and showed that this generally leads to a localization of the wavefunction, in sharp contrast with the Bloch-wave solution for a perfect crystal. This model has progressively been extended from its original solidstate physics scope [1,2,3,4] to a whole class of systems in which waves propagate in a disordered medium, as for example quantum-chaotic systems [5,6] and electromagnetic radiation [7,8,9]. However mathematically simple, the model predicts a wealth of interesting phenomena. In 1D, the wavefunction is always localized as recently observed in experiments using atomic matter waves in a disordered optical potential [10,11]; in 3D it predicts a phase transition between a localized (insulator) and a delocalized (metal) phase at a well defined mobility edge, the density of impurities or the energy being the control parameter.Despite the wide interest on the Anderson transition, few experimental results are available. In a crystal, it is very difficult to obtain the conditions for a clean observation of the Anderson localization. Firstly, one has no direct access to the electronic wavefunction and must rely on modifications of bulk properties like conductivity [2,12]. Secondly, it is difficult to reduce decoherence sources to a low enough level. We thus engineered a matter-wave system that is described by an Andersonlike model, which allows us to probe the physics of disordered systems in much better conditions than in condensed matter physics [13], namely: Almost no interaction between particles, weak absorption in the medium, no coupling with a thermal reservoir which could destroy localization and possibility of measuring the final quantum state of the system after a given interaction time. The system, the quasi-periodic kicked rotor [5,6,14,15], consists of cold cesium atoms exposed to a pulsed, offresonant, laser standing wave. The dynamics is thus effectively one-dim...

No abstract

We compare two different models of transport of light in a disordered system with a spherical Gaussian distribution of scatterers. A coupled dipole model, taking into account all interference effects, is compared to an incoherent model, using a random walk of particles. Besides the well-known coherent backscattering effect and a well pronounced forward lobe, the incoherent model reproduces extremely well all scattering features. In an experiment with cold atoms, we use the momentum recoil imparted on the center of mass of the sample as a partial probe of the light-scattering properties. We find that the force acting on the center of mass of the atoms is not well suited to exhibit the coherence effects in light propagation under multiple-scattering conditions.