Freezing, accelerating, and slowing directed currents in real time with superimposed driven lattices

We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures. Our results should allow for real-time control of cold thermal atomic ensembles in optical lattices but might also be useful as a design principle for targeted delivery of molecules or colloids in optical devices.

Figure 1

Schematic diagram of the setup and real-time control of directed transport. Top: Nontransporting state in the oscillating substrate lattice. Middle: Directed transport after switching on the carrier lattice. Bottom: Persistent transport after switching off the carrier lattice. Red particles perform diffusive motion whereas the blue ones are ballistic. The length and direction of the arrow indicate the speed and direction of the particle, respectively.

Figure 2

Mean transport velocity $\overline{v}$ of a particle ensemble as a function of time for four different cases. Case I: in presence of only substrate lattice (${\gamma }_V=0$). Case II: in presence of both substrate and superimposed carrier lattice ${\gamma }_V=1$. Case III: in presence of both lattices but carrier lattice switched off at $t=0.11t_{\mathrm{tot}}$ (blue dot) (${\gamma }_V=1$). Case IV: subsequent switches of the carrier lattice; blue dots show times ($t=0.10t_{\mathrm{tot}}$ and $t=0.25t_{\mathrm{tot}}$) where the carrier lattice is switched off, and green dots when it is switched on ($t=0.025t_{\mathrm{tot}}, t=0.175t_{\mathrm{tot}}$, and $t=0.30t_{\mathrm{tot}}$). At the final switch (red dot, $t=0.35t_{\mathrm{tot}}$), we switched also the relative driving phase $\varphi$ from $\varphi =\pi /2$ to $\varphi =-\pi /2$. Remaining parameters: $\mu =1.2665, \nu =\pi , \delta =\pi /2$, and $\varphi =\pi /2$.

Figure 3

The position (mod L) and velocity of all the $N$ particles (green) at (a) $t=0.04t_{\mathrm{tot}}$ in case I superposed on the PSOS P1 (black dots and lines) of the substrate lattice, (b) $t=0.42t_{\mathrm{tot}}$ in case III superposed on the PSOS P2 (black dots) corresponding to both the substrate and the carrier lattices, and (c) $t=0.95t_{\mathrm{tot}}$ in case IV superposed on the PSOS P3 (black dots) corresponding to both lattices but with $\varphi =-\frac{\pi }{2}$. Red solid lines denote the position of the FISCs whereas the red dashed lines indicate the location of the cantorus (see text). ${\mathcal{C}}_{\mathrm{U},\mathrm{C},\mathrm{L}}^i, i=1,2,3$, denotes the upper, central, and lower chaotic layer of P1, P2, and P3, respectively. (d) A zoom into the typical trajectory of a particle initiated at low velocity in the central chaotic sea of the PSOS P2 in (b), showing the particle's stickiness to the cantorus.