Transition between extended and localized states in a one-dimensional incommensurate optical lattice

Abstract

We study the localization properties of a one-dimensional incommensurate potential in the full quantum regime. In the system under consideration, and for amplitudes of the potential that are not too weak, the spectrum contains both localized and extended states, with one or more mobility edges. We show how these properties can be experimentally studied through the diffusion of wave packets in a one-dimensional incommensurate optical lattice.

Perfect absorption and no reflection in disordered photonic crystals

“…Cold atoms in disordered potentials have been extensively investigated [29,[53][54][55][56][57], especially in connection with Anderson localization [58]. Here, we are not interested in the atomic dynamics in random potentials per se, but only in the effects that a small disorder perturbing the periodic atomic distribution may have on the atomic crystal optical response, in much the same way as is done by the random perturbation of a speckle potential when superposed to an ideal optical lattice [58].…”

Bloch oscillations in lattice potentials with controlled aperiodicity

“…In contrast, such damping is absent in optical lattice systems which are inherently defect-free, allowing for the observation of a large number of oscillations [6][7][8]. Damping can however be induced by the introduction of disorder into the lattice potential, which can in principle be done with various techniques [15][16][17][18][19]. Also, in the case of quantum gases, a damping of Bloch oscillations arises from mean-field interactions between weakly interacting, Bose-condensed atoms [7,8,[20][21][22][23][24].…”

“…of Physics, Univ. Würzburg, Germany † present address: Photon Research Associates, Port Jefferson, NY we numerically investigate the dynamics of an atomic wave packet in a potential with a systematically degraded translational symmetry, considering two scenarios: The first is based on the use of a weak bichromatic potential [16] of a variable wavelength ratio, and the second considers scatterers (impurities) pinned at single sites of the potential [17]. We find that the damping strongly depends on the ratio of lattice constants in the bichromatic case and that even a small concentration of scatterers can lead to strong damping.…”

A glimpse of quantum phenomena in optical lattices

“…On the other hand, in real space, particles experience a complete absence of translational symmetry; quasi-periodic lattices have been proposed as a means of simulating disorder [30]. The nature of the eigenstates [30,31] and transport properties [26,27,30] of particles in quasi-periodic lattices, be they bosons or fermions, are expected to resemble those of particles in a random medium, which is the topic of §6.…”