Quantum Ratchets with Few Bands below the Barrier

We investigate directed motion in nonadiabatically rocked ratchet systems sustaining few bands below the barrier. Upon restricting the dynamics to the lowest $M$ bands, the total system-plus-bath Hamiltonian is mapped onto a discrete tight-binding model containing all the information both on the intrawell and interwell tunneling motion. A closed form for the current in the incoherent tunneling regime is obtained. In effective single-band ratchets, no current rectification occurs. We apply our theory to describe rectification effects in vortex quantum ratchets devices. Current reversals upon variation of the ac-field amplitude or frequency are predicted.

Figure 1

Ratchet potential with three bands below the barrier (shaded regions). The potential height is in units of the distance $\hslash {\omega }_0$ between the centers of the second and first band, and the length is in units of the period $L$.

Figure 2

Output velocity (or dc voltage for the vortex ratchet case) vs amplitude of the driving ac signal (ac current for vortex ratchet) for different driving frequencies $\Omega$. The dimensionless friction parameter $\alpha =2\pi \eta L^2/\hslash$ is chosen to be $\alpha =0.5$, describing moderate damping. Negative or positive ratchet currents are obtained upon appropriate tuning of the driving field parameters.

Figure 3

Same as in Fig. 2 for larger friction, $\alpha =2.0$. The main resonances occur at larger driving amplitudes.