Reflect magnetic control of NV center’s ground-state energy structure through quantum phase transitions in a three-level system

Abstract We theoretically investigate the quantum phase transitions of a hybrid quantum system consisting of an ensemble of nitrogen-vacancy (NV) centers coupled to two microwave cavity resonators. By leveraging the Zeeman effect with a static magnetic field, we achieve a tunable switch between different three-level Dicke model configurations. We map out the global ground-state phase diagram and identify three distinct operating regimes: (i) a V type regime characterized by the competition between two superradiant phases, (ii) an effective two-level regime emerging near the level-crossing point due to channel decoupling and (iii) a cascade Ξ type regime induced by level inversion. Particularly in the cascade regime, we analyze a mechanism of ‘sequential phase transition’, where the onset of the second superradiant phase is strictly contingent upon the condensation of the first channel. This mechanism leads to a nested structure in the phase diagram, which is fundamentally distinct from the phase competition observed in V type systems. Furthermore, by calculating the excitation spectra, we observe the emergence of soft modes at continuous critical points, establishing the second-order quantum nature of the relevant transitions. Our proposal provides a feasible solid-state platform for simulating multicritical phenomena and realizing controllable light–matter interactions.