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

Abstract

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, evaluating the gain/loss effects on various properties of the system in the context of non-Hermitian physics. Under periodic boundary conditions, we analytically give, via block diagonalization, the topological phase diagram, which undergoes a non-Hermitian gapless interval instead of a point of the Hermitian counterpart, causing that the complex band inversion is just a necessary but not sufficient condition for the topological phase transition. A gauge-independent non-Hermitian Wilson-line method is developed for numerically calculating the non-Hermitian Chern number of a subspace consisting of multiple complex bands, because the nodal loops of the lower/upper two bands of the Hermitian counterpart can be split into exceptional loops in this non-Hermitian model. Under open boundary conditions, we find that the conventional bulk-boundary correspondence does not break down, but the dynamics of the chiral edge states depend on the boundary selection, which may be used for the control of edge dynamics.

Non-Hermitian Absorption Spectroscopy

“…However, such a method is very hard to generalize to a generic case without PT symmetry. In fact, while there are practical proposals on how to realize non-Hermitian topological phases in cold atom systems [13,[43][44][45], such as non-Hermitian Weyl semimetals, it remains an outstanding open question of how to experimentally measure both the real and imaginary parts of energy spectra in a non-Hermitian cold atom system. Moreover, many non-Hermitian systems exhibit non-Hermitian skin effects (NHSEs) so that band structures under open boundary conditions (OBCs) are dramatically different from those under periodic boundary conditions (PBCs) [46][47][48][49][50].…”