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Laser-induced phase transition in ruby - Spontaneous breaking of the transition-saturation symmetry

В. Емелянов

Published Feb 1, 1987• 0 citations
OpenAlex

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Liouvillian spectral collapse in Scully-Lamb lasing: Non-equilibrium second-order phase transition with or without U(1)U(1)U(1) symmetry breaking
The paradigm of second-order phase transition and symmetry breaking for thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems. Despite the non-equilibrium nature of lasing, the laser threshold was compared with thermal phase transitions systems more than forty years ago. For instance, the Landau theory -- based on thermodynamical consideration -- has been used to characterize the Scully-Lamb laser model (SLLM), describing a single-mode laser without saturable absorbers. Accordingly, the laser threshold is a second-order phase transition, associated with a spontaneous symmetry breaking (SSB) of the U(1)U(1)U(1) symmetry of the model. To capture a genuine non-equilibrium, quantum, and dissipative phase transition of the SLLM, here we employ a Liouvillian superoperator formalism derived from a Lindblad master equation. Our results confirm that the U(1)U(1)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. This demonstrates the difference between the Liouvillian spectral collapse and a standard second-order phase transition with symmetry breaking. We characterize the new phenomena associated with the spectral collapse, such as the onset of a rather unusual multistability enabled (and not suppressed) by the very presence of fluctuations. This multistability, characterizing the dissipative and quantum origin of lasing, can be experimentally revealed by the presence of a dynamical hysteresis.