Localization properties of the asymptotic density distribution of a one-dimensional disordered system

Abstract

Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an initially narrow wave-packet released in a disordered potential will, at long time, decay exponentially on the scale of the localization length. However, the exact shape of the stationary localized distribution differs from a purely exponential profile and has been computed almost fifty years ago by Gogolin. Using the atomic quantum kicked rotor, a paradigmatic quantum simulator of Anderson localization physics, we study this asymptotic distribution by two complementary approaches. First, we discuss the connection of the statistical properties of the system's localized eigenfunctions and their exponential decay with the localization length of the Gogolin distribution. Next, we make use of our experimental platform, realizing an ideal Floquet disordered system, to measure the long-time probability distribution and highlight the very good agreement with the analytical prediction compared to the purely exponential one over 3 orders of magnitude.

arXiv comment10 pages, 8 figures

References in corpus (15)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Statistics of energy levels and eigenfunctions in disordered systems
• Statistical Signatures of Photon Localization
• Experimental observation of the Anderson transition with atomic matter waves
• Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves: Theory and Experiment
• Experimental Test of Universality of the Anderson Transition
• Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor
• Field theory of the quantum kicked rotor
• Controlling symmetry and localization with an artificial gauge field in a disordered quantum system
• Quantum simulation of disordered systems with cold atoms
• Ehrenfest time in the weak dynamical localization
• Ratchet Effect in the Quantum Kicked Rotor and its Destruction by Dynamical Localization
• Return to the Origin as a Probe of Atomic Phase Coherence
• Experimental observation of time singularity in classical-to-quantum chaos transition
• Experimental realization of an ideal Floquet disordered system