Controlling the Ratchet Effect for Cold Atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.

Figure 1

Time dependence of the ratchet current for various $P,\tilde{\hslash }$. In (a) $\tilde{\hslash }=1.001\pi$ with no directed transport. In (b) $\tilde{\hslash }=0.7\pi (r/s=7/40)$, (c) $\tilde{\hslash }=2.625\pi (r/s=21/32)$ and (d) $\tilde{\hslash }=1.5\pi (r/s=3/8)$, and transport occurs with $P$-dependent rates and direction. For reading in gray-scale, the $P$ values for each panel are reported below in the sequence of curves from top to bottom, in (a) at $t\approx 15$ and for other panels at all times. (a) $P=6.0$ (magenta), 5.0 (brown), 4.0 (cyan) 3.0 (blue), 2.0 (green), 1.0 (red), 0.5 (black): in (b) $P=5.0$ (brown), 1.0 (red), 2.0 (green), 0.5 (black), 6.0 (magenta), 3.0 (blue), 4.0 (cyan); in (c) $P=8.0$ (magenta), 7.0 (brown), 4.0 (blue), 3.0 (green), 2.0 (red), 1.0 (black), 5.0 (cyan); in (d) $P=4.0$ (cyan), 3.0 (blue), 5.0 (brown), 2.0 (green), 1.0 (red), 0.5 (black), 6.0 (magenta).

Figure 2

Ratchet current $⟨k⟩$ as a function of $\tilde{\hslash }/\pi$ after 200 kicks, with the potential parameter $\alpha =0.3$, and the potential strength $P$ indicated in each panel. Main resonances appear in (a) with low $P$. As $P$ increases in (b), (c), and (d), full chaos is being developed (see Fig. 3) and significant ratchet currents due to higher-order quantum resonances emerge.

Figure 3

Classical phase-space structures for the kicked ratchet map for $\alpha =0.3$ showing regular islands embedded in the chaotic sea for (a) $K=0.25\pi$, (b) $K=0.55\pi$, and (c) $K=0.70\pi$. In panel (d) $K=0.8\pi$ and full chaos is reached.

Figure 4

Acceleration rate $\Gamma$ as a complicated function of the potential strength $P$ for different $\tilde{\hslash }$. The inset shows the number of Floquet bands below the potential barrier as a function of $K$, fitted empirically as $n\propto \sqrt{K}$.