Quantum anomalous Hall effect with cold atoms trapped in a square lattice

We propose an experimental scheme to realize the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental setups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detection through light Bragg scattering of the edge and bulk states with which one can determine the topological phase transition from usual insulating phase to quantum anomalous Hall phase.

Figure 1

(A) Fermions trapped in a 2D anisotropic square optical lattice. Due to the different on-site trapping frequencies, the square lattice is divided into two sublattices $A$ and $B$. (B) The local orbitals are in the ${\mathrm{e⃗}}_1$ and ${\mathrm{e⃗}}_2$ directions.

Figure 2

Gapped bulk states (black lines) and gapless edge states [straight blue dashed lines in panels (a) and (c) and straight red solid lines in panels (b) and (d), respectively] on the boundaries $x=0$ (a, c) and $x=L$ (b, d). Parameters in panels (a) and (b) are $M=0$, ${\varphi }_0=\pi /2$, and in (c) and (d) are $M=0$, ${\varphi }_0=-\pi /2$. The energy spectra are plotted in units of $2.5{\Delta }_0$. The chirality of edge states indicates the Chern number $C_1=+1$ for ${\varphi }_0=\pi /2$ and $C_1=-1$ for ${\varphi }_0=-\pi /2$.

Figure 3

Schematic of light Bragg scattering (a) and dynamical structure for the cases in which the system is in the topological phase (b, c) and in the insulating phase (d).