Phase diagram of the anisotropic Anderson transition with the atomic kicked rotor: theory and experiment

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.

Scaling properties of dynamical localization in monochromatically perturbed quantum maps: Standard map and Anderson map

“…They explained their results by applying self-consistent mean field theory (SCT) to the monochromatically perturbed SM, and they obtained A ∝ ( K ) 2 , but D ∝ K , which is inconsistent with Eq. (11). A modified version of SCT of the localization naturally leading to the result Eq.…”

“…Their results are also interpreted by the self-consistent theory (SCT) of the weak localization in three dimensional disordered system (3DDS) [4][5][6][7][8][9][10][11]. Further, they recently observed the localization phenomenon in the SM driven by coherent monochromatic perturbation [15].…”

“…A typical example of the former is one-dimensional disordered systems (1DDS) [1,2], and the latter one is the quantum standard map (SM) [3]. It has been shown that the localization of the wavepacket can be delocalized by applying dynamical perturbation composed of a few number of coherent modes [4][5][6][7][8][9][10][11]. If the number of the modes is more than two, the delocalization takes place through a localizationdelocalization transition (LDT) accompanied by remarkable critical phenomena as the perturbation strength is increased.…”

Return to the Origin as a Probe of Atomic Phase Coherence

“…Parameters are K = 12, k = 1.5 and a = 0.04. arXiv:1606.07237v1 [cond-mat.dis-nn] 23 Jun 2016 the other hand, the atomic quantum kicked rotor (QKR), a model system for quantum chaos [19], has played a key role in the observation of dynamical localization, a suppression of the classical chaotic diffusion in momentum space by quantum interference [20,21], analog to Anderson localization [22]. By adding modulation frequencies [23,24], "quantum simulations" [25] of multidimensional Anderson models have been realized in 2D [26] and 3D [27][28][29][30][31] systems, where the metal-insulator transition has been completely characterized.…”

At the edge of mobility

“…The latter has been measured in kicked-rotor systems but not yet in real-space matter waves 13,14 . Presently, the method developed by Semeghini et al 3 is not sufficiently precise to determine the value of this exponent and new strategies should be developed.…”