In the standard quantum Rabi model, increasing the coupling between light and matter drives a superradiant phase transition — coherent behavior emerges when the coupling exceeds a critical threshold. Stronger coupling, more coherence.
Parametric amplification with two-photon decay inverts this. Coherent effects appear only at low coupling strengths. Increase the coupling and the superradiance dies. The phase diagram is upside down.
The mechanism is the competition between parametric amplification (which generates pairs of photons coherently) and two-photon dissipation (which removes them). At low coupling, the amplification wins and a coherent superradiant state forms. At high coupling, the atom-photon interaction disrupts the coherent pair creation, and the system falls back to an incoherent state.
The transition is not simple. The model exhibits both first-order and second-order dissipative phase transitions, separated by a tricritical point — a special value of the parameters where the character of the transition changes from continuous to discontinuous. The tricriticality arises from the intrinsic nonlinearity of the Rabi interaction combined with the two-photon nature of the dissipation. At the tricritical point, the critical exponents take specific universal values, classifying the transition into known universality classes.
The inversion is structural, not accidental. It follows from the fact that the superradiance is driven by the parametric process, not the light-matter coupling. The coupling that normally enables coherence instead competes with the coherence's actual source. Making the system more interactive makes it less ordered.