Topological superfluid transition induced by a periodically driven optical lattice

We propose a scenario to create a topological superfluid in a periodically driven two-dimensional square optical lattice. We study the phase diagram of a spin-orbit coupled $s$-wave pairing superfluid in a periodically driven two-dimensional square optical lattice. We find that a phase transition from a trivial superfluid to a topological superfluid occurs when the potentials of the optical lattices are periodically changed. The topological phase is called the Floquet topological superfluid and can host Majorana fermions.

Figure 1

The phase diagram and the band structures of the system. (a) The mass $M\left(z\right)$ as a function of $z$. Region I with $M\left(z\right)<0$ is a trivial superfluid, while region II with $M\left(z\right)>0$ is a topological superfluid. The band structures of the effective Hamiltonian (10) in a striped geometry with 300 sites in the $x$ direction are shown in (b)–(d), corresponding to the points A ($z=0$), B ($z=0.299$), and C ($z=0.4$) in (a), respectively. The other parameters are $t_0=1,\lambda =1.6,{\psi }_s=-0.15,\hslash \omega =6.0,$ and $\mu =-3.91$.