Controlling directed atomic motion and second-order tunneling of a spin-orbit-coupled atom in optical lattices

We theoretically explore the tunneling dynamics for the tight-binding model of a single spin-orbit-coupled atom trapped in an optical lattice subjected to lattice shaking and to time-periodic Zeeman field. By means of analytical and numerical methods, we demonstrate that the spin-orbit (SO) coupling adds some results to the tunneling dynamics in both multiphoton resonance and far-off-resonance parameter regimes. When the driving frequency is resonant with the static Zeeman field (multiphoton resonances), we obtain an unexpected dynamical localization (DL) phenomenon where the single SO-coupled atom is restricted to making perfect two-site Rabi oscillation accompanied by spin flipping. By using the unconventional DL phenomenon, we are able to generate a ratchetlike effect which enables directed atomic motion towards different directions and accompanies periodic spin flipping under the action of SO coupling. For the far-off-resonance case, we show that by suppressing the usual intersite tunneling alone, it is possible to realize a type of spin-conserving second-order tunneling between next-nearest-neighboring sites, which is not accessible in the conventional lattice system without SO coupling. We also show that simultaneous controls of the usual intersite tunneling and the SO-coupling-related second-order tunneling are necessary for quasienergies flatness (collapse) and completely frozen dynamics to exist. These results may be relevant to potential applications such as spin-based quantum information processing and design of spintronics devices.