N-photon solutions to the two-qubit quantum Rabi model

TL;DR

This paper explores specific multi-photon solutions in the two-qubit quantum Rabi model, revealing unique eigenenergy properties and potential applications in quantum information processing under ultrastrong coupling regimes.

Contribution

It introduces novel N-photon dark state solutions with constant eigenenergy and level crossings, expanding understanding of the two-qubit quantum Rabi model's spectral properties.

Findings

Existence of N-photon dark states with constant eigenenergy.

Level crossings within the same parity subspace at N=3.

Asymptotic solutions with eigenenergy proportional to photon number at strong coupling.

Abstract

We studied the two-qubit quantum Rabi model and found its dark state solutions with at most N photons. One peculiar case presents when $N=3$, which has constant eigenenergy in the whole coupling regime and leads to level crossings within the same parity subspace. We also discovered asymptotic solutions with at most $N=2i+3$ $(i=1,2,3,\dots)$ photons, and constant eigenenergy $N\hbar \omega$ when coupling $g$ becomes much larger than photon frequency $\omega$. Although generally all photon number states are involved in the two-qubit quantum Rabi model, such $N$-photon solutions exist and may have applications in quantum information processing with ultrastrong couplings.