Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices

Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model and evaluate the gain/loss effects on various properties of the system, revealing the interplay of the non-Hermiticity and the spin-orbit coupling. Under periodic boundary conditions, we analytically obtain the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point that the Hermitian counterpart encounters for a topological phase transition. We also unveil that the band inversion is just a necessary but not sufficient condition for a topological phase in two-level spin-orbit coupled non-Hermitian systems. Because the nodal loops of the upper or lower two dressed bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model, a gauge-independent Wilson-loop method is developed for numerically calculating the Chern number of multiple degenerate complex bands. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down with only on-site gain/loss due to the lack of non-Hermitian skin effect, but the dissipation of chiral edge states depends on the boundary selection, which may be used in the control of edge-state dynamics. Given the technical accessibility of state-dependent atom loss, this model could be realized in current cold-atom experiments.