Robust Topological Feature against Non-Hermiticity in Jaynes–Cummings Model

The Jaynes–Cummings Model (JCM) is a fundamental model and building block for light-matter interactions, quantum information and quantum computation. The present work analytically analyzes the topological feature manifested by the JCM in the presence of non-Hermiticity which may arise from dissipation and decay rates. Indeed, the eigenstates of the JCM are topologically characterized by spin windings in 2D plane. The non-Hermiticity tilts the spin-winding plane and induces an out-of-plane component, while the topological feature is maintained. In particular, besides the invariant spin texture nodes, the study reveals a non-Hermiticity-induced reversal transition of the tilting angle and spin winding direction with a fractional phase gain at gap closing, a partially level-independent reversal transition without gap closing, and a completely level-independent super-invariant point with untilted angle and also without gap closing. The result demonstrates that the topological feature is robust against non-Hermiticity, which may be favorable in practical applications. On the other hand, one may conversely make use of the disadvantageous dissipation and decay rates to reverse the spin winding direction, which may add a controlled way for topological manipulation of quantum systems in light-matter interactions.