Dissipative quantum phase transitions in electrically driven lasers

Embedding quantum dot circuits into microwave cavities has emerged as a novel platform for controlling photon emission statistics by electrical means. With such a circuit version of the Rabi model, we reveal previously undefined quantum phase transitions in electrically driven lasing regimes, which do not require deep strong light-matter couplings. For one-photon interaction, the scaling analysis indicates that the system undergoes a continuous phase transition from thermal to coherent photon emissions. Going beyond this, a discontinuous quantum phase transition from superbunched to coherent states in two-photon processes, accompanied by the bistability within a mean-field theory, is predicted. Both the order of phase transitions and the critical electron-photon coupling can be easily controlled by an electric field, while the tunneling current can be used as a fingerprint of such transitions. Our prediction, along with its extension to multiphoton processes, represents a key step towards accessing lasing phase transitions.