Site-selective particle deposition in periodically driven quantum lattices

We demonstrate that a site-dependent driving of a periodic potential allows for the controlled manipulation of a quantum particle on length scales of the lattice spacing. Specifically we observe for distinct driving frequencies a near depletion of certain sites which is explained by a resonant mixing of the involved Floquet-Bloch modes occurring at these frequencies. Our results could be exploited as a scheme for a site-selective loading of, e.g., ultracold atoms into an optical lattice.

Figure 1

(a) Snapshot of a site-dependently driven lattice with lattice site occupations $n_s$. Shaded barriers indicate the barriers' equidistant equilibrium positions. (b) Time evolution of lattice site populations for an initial Gaussian of width $\sigma =20\pi$ in a lattice with three barriers per unit cell with phases $(0,\pi ,0)$. Panels (c), (d), and (e) depict populations of the first three lattice sites [encompassed by a black rectangle in panel (b)] for phases of the central barrier in each unit cell of $\pi$ (c), $0.2\pi$ (d), and 0 (e). The remaining parameters are $L=10,V_0=1.0,\omega =1.0,A=1.0,m=1.0,\hslash =1.0$, and $\Delta =0.5$.

Figure 2

Setup consisting of three barriers with phases ${\delta }_s=(0,\pi ,0)$ for periodic boundary conditions. (a) Time evolution of the lattice site occupation $n_s\left(mT\right)$; panels (b) and (c) show the same quantity but only the three (b) or two (c) most occupied FBMs are taken into account. (d) Position representation of the three most occupied FBMs. The remaining parameters are the same as those in Fig. 1.

Figure 3

(a) Population of the $s=0$ lattice site for a setup containing three lattice sites with phases $(0,\pi ,0)$ and periodic boundary conditions $\left(\kappa =0\right)$ for different driving frequencies $\omega$. (b) Extract of $n_{\text{max}}\left(\omega \right)$ (black) together with the overlap of the FGS with a uniform state ${\Phi }_u$ (blue). Vertical lines are by Eq. (8) predicted resonances for $n=1$ (solid) and $n=2$ (dashed). (c) Maximal population of any of the three lattice sites $n_{\text{max}}\left(\omega \right)$ which is reached within the first 400 driving periods. (d) QE spectrum (small arrow indicates the FGS). The remaining parameters are the same as those in Fig. 1.

Figure 4

(a) Time evolution of the lattice site occupation $n_s\left(mT\right)$ for the resonant case $\omega =2.74$. (b) $n_s\left(mT\right)$ for $s=0,1,2$ [encompassed by a black rectangle in panel (a)]. (c) Same as in panel (b) but restricted to $\kappa =0$. The $s=0$ and $s=1$ curves in panels (b) and (c) are barely distinguishable. The remaining parameters are the same as those in Fig. 1.