Directed transport in driven optical lattices by gauge generation

We examine the dynamics of ultracold atoms held in optical-lattice potentials. By controlling the switching of a periodic driving potential we show how a phase-induced renormalization of the intersite tunneling can be used to produce directed motion and control wave-packet spreading. We further show how this generation of a synthetic gauge potential can be used to split and recombine wave packets, providing an attractive route to implementing quantum computing tasks.

Figure 1

Response of a Gaussian wave packet (${\sigma }_0=4$) to a periodic driving potential, $\omega =16J$. (a) Wave-packet expansion under cosinusoidal driving; from top to bottom $K/\omega =0,1,2,2.4$. For $K/\omega =2.4$, CDT occurs, and the expansion is suppressed. (b) Real component of $J_{\mathit{eff}}$ extracted from the expansion curves for cosinusoidal (black circles) and sinusoidal (red squares) driving. The curves show the theoretical prediction obtained from Eq. (3). (c) Displacement of a wave packet under sinusoidal driving in units of the lattice spacing. For $K/\omega =0$ and $2.4$ no displacement occurs; otherwise, it increases linearly with time. (d) As in (b), for the wave-packet velocity, given in units of $d_L/T$ where $d_L$ is the lattice spacing. Vertical blue arrows mark the driving parameters $K/\omega =\pi /2$ (dispersionless directed transport) and $K/\omega =2.404$ (complete suppression of dynamics).

Figure 2

Density plot of the motion of a wave packet under sinusoidal driving. Initially $K/\omega =\pi /2$ to induce dispersionless transport. $K/\omega$ is then set to $2.404$ to freeze the motion and finally to $-\pi /2$ to reverse it. The vertical dotted lines indicate the times at which $K/\omega$ is changed.

Figure 3

Density plot of a two-component wave packet under sinusoidal driving. Initially $K/\omega =\pi /2$ and the wave packet splits apart. Its motion is then halted and reversed as before to bring about a collision. The interaction, $g=0.5J$, causes the final state to be asymmetric.

Figure 4

(a) Expansion of a phase-incoherent wave packet, obtained by averaging over 200 random realizations of the onsite phases. Driving parameters are $n=1$ and $K/\omega =0.8$. The density profile is shown in time steps of $24T$, showing the formation of a double-peak structure as the wave packet spreads. (b) Symbols show results obtained from simulations for the real component of the effective tunneling, $\text{Re}\left[J_{\mathit{eff}}\right]$ (black circles), which controls the rate of wave-packet spreading, and velocity (red squares), given in units of $d_L/T$. Dashed lines show the analytical results. The minimum values of $\text{Re}\left[J_{\mathit{eff}}\right]$ align with the maximum velocity and vice versa.