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arXiv:cond-mat/0506415 · Physical Review A

Cold-atom optical lattices as quantum analog simulators for aperiodic one-dimensional localization without disorder

V. W. Scarola, S. Das Sarma

Published Apr 28, 2006• 15 citations
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Abstract

Cold-atom optical lattices allow for the study of quantum localization and mobility edges in a disorder-free environment. We predict the existence of an Anderson-like insulator with sharp mobility edges in a one-dimensional nearly periodic optical lattice. We show that the mobility edge manifests itself as the early onset of pinning in center of mass dipole oscillations in the presence of a magnetic trap, which should be observable in optical lattices.

DOI
10.1103/physreva.73.041609

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Cold-atom optical lattices allow for the study of quantum localization and mobility edges in a disorder-free environment. We predict the existence of an Anderson-like insulator with sharp mobility edges in a one-dimensional nearly periodic optical lattice. We show that the mobility edge manifests itself as the early onset of pinning in center of mass dipole oscillations in the presence of a magnetic trap, which should be observable in optical lattices.
A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, in a quasiperiodic system, the localization transition can occur at a finite detuning strength and SPMEs become possible. In this Letter, we find experimental evidence for the existence of such a SPME in a one-dimensional quasiperiodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime.
We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species or spin state and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable a nearly perfect experimental control of the disorder, while the possibility of modeling the scattering potentials by a set of pointlike ones allows an exact theoretical analysis. This is illustrated by a detailed analysis of the one-dimensional case.
Quasiperiodic lattices have been widely studied in cold atoms, which make one study extended-Anderson localization transition in one-dimensional (1D) or two-dimensional (2D) systems. In 2008, Inguscio's group prepared one-dimensional quasiperiodic lattice in cold atomic system and observed Anderson localization, which promoted the theoretical and experimental studies of quasiperiodic systems. Later, Bloch's group observed the many body localization in their prepared 1D and 2D quasiperiodic lattices. Recently, they also successfully observed the mobility edge and many body localization in a system with mobility edge in quasiperiodic lattices. These cold atom experiments have promoted the researches of many body localization and mobility edge. Quasiperiodic lattices have become a platform and its effects on many physical phenomena are being extensively studied, which can be expectantly observed in cold atomic experiments. This paper is based on the authors' some related work and briefly review some recent studies on the 1D quasiperiodic lattices, including some important cold atom experiments, some important properties of the quasiperiodic lattices and their effects on some physical phenomena, such as topological states.
We investigate the localization transition in a one-dimensional extended Aubry–André–Harper (AAH) model, emphasizing its implementation as a quantum simulator in ultracold atomic optical lattices. In the single-particle case, quasi-periodic hopping modulation allows the localization transition point to be clearly observed even for small system sizes. By driving the system into strongly Anderson localized states immediately after the transition, we observe a sharp many-body localization (MBL) transition upon introducing interactions, with the MBL transition point closely approaching that of Anderson localization. To demonstrate the effects of interactions, we map out a global phase diagram and find that critical states in this model are easily thermalized. Contrary to previous studies where enhanced interactions significantly promoted thermalization, we find that increasing interactions does not notably shift the MBL transition point. Importantly, our setup offers a practical and experimentally accessible platform for studying sharp MBL transitions using ultracold atoms in optical lattices, bridging MBL physics with advances in quantum optics and cold-atom technologies.
We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.
Observations of center-of-mass dynamics offer a straightforward method to identify strongly interacting quantum phases of atoms placed in optical lattices. We theoretically study the dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center-of-mass motion even with insulating states in the center. We identify short- and long-time-scale mechanisms for edge-state transport in insulating phases. We also argue that the center-of-mass velocity can aid in identifying a Bose-glass phase. Our zero-temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center-of-mass dynamics expected at nonzero temperature.