Anisotropic qubit-photon interactions inducing multiple antibunching-to-bunching transitions of photons

We investigate photon correlations in the open anisotropic quantum Rabi model via quantum dressed master equation. Multiple antibunching-to-bunching transitions are generally exhibited at deep-strong qubit-photon coupling, which becomes vanishing in the standard open quantum Rabi model. The observed two-photon statistics can be well described analytically within a few lowest eigenstates at low temperatures. It is revealed that the additional photon antibunching effect mainly originates from the selection rule of the correlation-measurement-induced eigenstate transitions. Furthermore, we also unravel the phenomena that higher-order correlation function lifts up dramatically once passing the crossing point of excited states, which is attributed to the on-off switch of dominant cooperative transition with level crossing. We hope these results may fertilize the analysis of the nonclassical photon statistics in anisotropic coupled qubit-photon systems.