Critical State of the Anderson Transition: Between a Metal and an Insulator

Laboratoire Kastler Brossel, UPMC-Paris 6, ENS, CNRS
Physical Review Letters (Impact Factor: 7.51). 08/2010; 105(9):090601. DOI: 10.1103/PHYSREVLETT.105.090601
Source: arXiv


Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the time evolution of an initially localized wave packet and show that it displays at the critical point a scaling invariance characteristic of this second-order phase transition. The shape of the momentum distribution at the critical point is found to be in excellent agreement with the analytical form deduced from the self-consistent theory of localization.

Full-text preview

Available from: ArXiv
  • Source
    • "Fortunately, one can find other systems also described by the Anderson localization physics, which are not a direct transposition of the condensed matter system, but rely on the profound analogy between quantum chaotic systems and disordered systems [7]. Using the quasiperiodic kicked rotor (QpKR)—first studied in [8]— an effectively three-dimensional (3D) variant of the paradigmatic system of quantum chaos [9] [10], the Anderson transition has been observed, its critical exponent measured experimentally [11] [12], its critical wavefunction characterized [13], and its class of universality firmly established [14], making this system an almost ideal environment to study Anderson-type quantum phase transitions 5 . "
    [Show abstract] [Hide abstract]
    ABSTRACT: We realize experimentally a cold-atom system, the quasiperiodic kicked rotor, equivalent to the three-dimensional Anderson model of disordered solids where the anisotropy between the x direction and the y – z plane can be controlled by adjusting an experimentally accessible parameter. This allows us to study experimentally the disorder versus anisotropy phase diagram of the Anderson metal–insulator transition. Numerical and experimental data compare very well with each other and a theoretical analysis based on the self-consistent theory of localization correctly describes the observed behavior, illustrating the flexibility of cold-atom experiments for the study of transport phenomena in complex quantum systems.
    Full-text · Article · Jun 2013 · New Journal of Physics
  • Source
    • "A burst of interest in the subject was recently seen, driven by the demonstration that these questions could be studied experimentally and theoretically with an unprecedented degree of cleanness and precision using ultracold atoms. The study of the problem in the absence of interactions led to impressive results, concerning both AL [3] [4] [5] [6] [7] [8] and the Anderson transition [9] [10] [11] [12], observed in three-dimensional (3D) systems. The effects of interactions on ultracold bosons turned out to be very well modelled by mean-field approaches [13] [14], in contrast to fermionic systems where such a simplification of the corresponding many-body problem is not possible. "
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short time dynamics, and shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system behaviour at longer times.
    Full-text · Article · Dec 2012 · New Journal of Physics
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Sanli Faez onderzocht de voortplanting van golven in wanordelijke materialen. Hij bestudeerde, zowel theoretisch als experimenteel, uitingen van Anderson-lokalisatie met klassieke golven, zoals licht en ultrageluid. Anderson-lokalisatie verwijst naar de onderdrukking van diffusie in wanordelijke materie als gevolg van interferentie. Deze overgang van geleider naar isolator werd vijftig jaar geleden ontdekt door Philip Anderson in het kader van elektronentransport in metalen.
    Full-text · Article ·
Show more