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.
Highlights
The interplay of disorder and quantum interference has been an important subject in physics for more than 50 years
The Anderson metal-insulator transition is still very difficult to study in such systems, because Anderson localization requires a very strong disorder and – the cold atomic samples being prepared in the absence of disorder – the energy distribution of the atoms unavoidably spreads across the socalled mobility edge, an energy threshold separating localized and extended eigenstates
Using the quasiperiodic kicked rotor (QpKR) [7], an effectively 3D variant of the paradigmatic system of quantum chaos [8], the Anderson transition has been observed, its critical exponent measured experimentally [9, 10], its critical wavefunction characterized [11], and its class of universality firmly established [12], making this system an almost ideal environment to study Anderson type quantum phase transitions. One advantage of this cold atom chaotic system as compared to other disordered systems is that the disorder can be controlled very precisely: the mean free path and the anisotropy are two experimentally tunable parameters. This allows us to present in this work an experimental study of the disorder vs anisotropy phase diagram of the Anderson transition, as well as an analytical description of these properties based on the self-consistent theory of Anderson localization, which brings another important brick to our detailed knowledge on the Anderson metal-insulator transition
Summary
The interplay of disorder and quantum interference has been an important subject in physics for more than 50 years. Using the quasiperiodic kicked rotor (QpKR) [7], an effectively 3D variant of the paradigmatic system of quantum chaos [8], the Anderson transition has been observed, its critical exponent measured experimentally [9, 10], its critical wavefunction characterized [11], and its class of universality firmly established [12], making this system an almost ideal environment to study Anderson type quantum phase transitions One advantage of this cold atom chaotic system as compared to other disordered systems is that the disorder can be controlled very precisely: the mean free path and the anisotropy are two experimentally tunable parameters. This allows us to present in this work an experimental study of the disorder vs anisotropy phase diagram of the Anderson transition, as well as an analytical description of these properties based on the self-consistent theory of Anderson localization, which brings another important brick to our detailed knowledge on the Anderson metal-insulator transition
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