“…Interestingly, the reaction coordinate mapping tries to theoretically establish the bridge between the SBM and the coupled qubit-resonator system [16,[30][31][32][33][34]. Recently, two-photon based quadratic interaction in HQSs, e.g., two-photon Rabi model, has attracted increasing attention, which has practical correspondence in the circuit-QED platform [35,36], and theoretically leads to spectral collapse [37,38], quantum phase transition [39][40][41], ultrafast charging quantum battery [42,43] and enhancement of superradiant spontaneous emission [44]. Moreover, such nonlinear interactions play a crucial role in modeling the electric current based on the quantum dot-vibration hybrid model [45].…”