Bloch oscillations of spin-orbit-coupled cold atoms in an optical lattice and spin current generation

We study the Bloch oscillation dynamics of a spin-orbit-coupled cold atomic gas trapped inside a one-dimensioanl optical lattice. The eigenspectra of the system is identified as two interpenetrating Wannier-Stark ladder. Based on that, we carefully analyzed the Bloch oscillation dynamics and found out that intraladder coupling between neighboring rungs of Wannier-Stark ladder give rise to ordinary Bloch oscillation while interladder coupling lead to small amplitude high frequency oscillation superimposed on it. Specifically spin-orbit interaction breaks Galilean invariance, which can be reflected by out-of-phase oscillation of the two spin components in the accelerated frame. The possibility of generating spin current in this system are also explored.