Nonequilibrium topological phase transitions in two-dimensional optical lattices

Recently, concepts of topological phases of matter are extended to nonequilibrium systems, especially periodically driven systems. In this paper, we construct an example which shows nonequilibrium topological phase transitions using ultracold fermions in optical lattices. We show that the Rabi oscillation has the possibility to induce nonequilibrium topological phases which are classified into time-reversal-invariant topological insulators for a two-orbital model of alkaline-earth-metal atoms. Furthermore, we study the nonequilibrium topological phases using time-dependent Schrieffer–Wolff-type perturbation theory, and we obtain an analytical expression to describe the topological phase transitions from a high-frequency limit of external driving fields.

Figure 1

The effective level ${\Delta }_{\mathrm{eff}}$ of the two-level system subject to the Rabi oscillation. Here we set the parameters as $\Delta =1$ (the energy unit) and $\omega =3$.

Figure 2

The quasienergy spectrum of the effective Hamiltonian. Here we set the parameters as $C_1=C_2=0.05,M=1$ (the energy unit), $B_1=0.25,B_2=0.15,A_{11}=A_{23}=0.15,A_{13}=A_{21}=0.25,\varphi =0$, and $\omega =3$. The figures show the quasienergy at (a) ${\Omega }_R/2=0$, (b) ${\Omega }_R/2=0.5$, (c) ${\Omega }_R/2=0.75$, and (d) ${\Omega }_R/2=1.25$.

Figure 3

Plots of some components of the effective Hamiltonian. The left figure is the ${\sigma }_1\otimes {\tau }_2$ component calculated by the perturbation theory [Eq. (34)], and the right figure is that of the numerical result for the effective Hamiltonian. The parameters of the Hamiltonian are the same as in Fig. 2.

Figure 4

Plots of some components of the effective Hamiltonian. The left figure is the ${\sigma }_3\otimes {\tau }_0$ component calculated by the perturbation theory [Eq. (33)], and the right figure is that of the numerical result for the effective Hamiltonian. The parameters of the Hamiltonian are the same as in Fig. 2.