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

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.

Figure 1

(Color online) Top panel: Lyapunov exponent vs energy for the nearly periodic Harper model, Eq. (1) with $V=0.5$, $ϵ=0.005$, and $\Omega =0$. The solid (dot-dashed) line shows the disorder-free, $V_D=0$ (disordered, $V_D=1$) case. Bottom panel: Level number vs energy of the disorder-free, nearly periodic Harper model for two characteristic values of $ϵ$ with $V=0.5$, $N=3000$, and $\Omega =0$. The lower curve is shifted downward by 100 levels for clarity.

Figure 2

(Color online) The local Lyapunov exponent vs energy for the same parameters as the upper panel of Fig. 1, but with an additional parabolic confinement $\Omega ={10}^{-5}$ and no disorder, $V_D=0$. The inset shows the normalized density of the same system as a function of the lattice number for several different chemical potentials.

Figure 3

(Color online) The long-time average of the center-of-mass position as a function of the chemical potential after an initial displacement of three sites, $\Delta =-3$, with no disorder, $V_D=0$. The dashed line is calculated from the bare tight-binding model with no secondary lattice, $V=0$, and $\Omega ={10}^{-5}$. B.E. labels the upper band edge. The solid line is calculated for the same parameters, but with $V=0.5$. The early onset of the gapless insulator occurs at the upper mobility edge, labeled M.E., while the upper band edge remains at $\mu =2$.