Hidden Single-Qubit Topological Phase Transition without Gap Closing in Anisotropic Light-Matter Interactions

Conventionally the occurrence of topological phase transitions (TPTs) requires gap closing, whereas there are also unconventional cases without need of gap closing. Although traditionally TPTs lie in many-body systems in condensed matter, both cases of TPTs may find analogs in few-body systems. Indeed, the ground-state node number provides a topological classification for single-qubit systems. While the no-node theorem of spinless systems is shown to restrict the fundamental quantum Rabi model in light-matter interactions, it is demonstrated that the limitation of the no-node theorem can be broken not only in small counter-rotating terms (CRTs) but also in the large-CRT regime, which striates a rich phase diagram with different TPTs. While these transitions are mostly accompanied with gap closing and parity reversal, a hidden node-phase transition is revealed that has neither gap closing nor parity change, which turns out to be an analog of the unconventional TPT in condensed matter. A hysteresis sign for the unconventional TPT is unveiled via the transition from phase squeezing to amplitude squeezing in the gapped phase. The imprints in the Wigner function are also addressed. The clarified mechanisms provide some special insights for the subtle role of the CRTs.