Liouvillian spectral collapse in the Scully-Lamb laser model

Abstract

Phase transitions of thermal systems and the laser threshold were first connected more than forty years ago. Despite the nonequilibrium nature of the laser, the Landau theory of thermal phase transitions, applied directly to the Scully-Lamb laser model (SLLM), indicates that the laser threshold is a second-order phase transition, associated with a $U(1)$ spontaneous symmetry breaking (SSB). To capture the genuine nonequilibrium phase transition of the SLLM (i.e., a single-mode laser without a saturable absorber), here we employ a quantum theory of dissipative phase transitions. Our results confirm that the $U(1)$ SSB can occur at the lasing threshold but, in contrast to the Landau theory and semiclassical approximation, they signal that the SLLM "fundamental" transition is a different phenomenon, which we call Liouvillian spectral collapse; that is, the emergence of diabolic points of infinite degeneracy. By considering a generalized SLLM with additional dephasing, we witness a second-order phase transition, with a Liouvillian spectral collapse, but in the absence of symmetry breaking. Most surprisingly, the phase transition corresponds to the emergence of dynamical multistability even without SSB. Normally, bistability is suppressed by quantum fluctuations, while in this case, the very presence of quantum fluctuations enables bistability. This rather anomalous bistability, characterizing the truly dissipative and quantum origin of lasing, can be an experimental signature of our predictions, and we show that it is associated with an emergent dynamical hysteresis.