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Foundations of Physics

Emergence of Classical Radiation Fields through Decoherence in the Scully-Lamb Laser Model

Julio R. Gea-Banacloche

Published Apr 1, 1998• 14 citations
Publisher
DOI
10.1023/a:1018729904161

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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.

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Conventional laser theory deals with discrete ‘cavity modes’ and introduces artificial mechanisms to simulate radiation field losses caused by beam extraction. A more realistic model of a laser with a transmitting window, previously investigated by Lang, Scully and Lamb, is reanalysed semiclassically. In the previous work, the continuous radiation field spectrum was treated as the limit of a discrete but very dense spectrum of modes, and the narrowness of the laser linewidth was attributed to the locking together of these modes. Working entirely within the continuous spectrum, we find that the treatment is considerably simplified, leading to an explicit solution for single-quasimode operation within the linear approximation which exhibits the role of the excitation conditions in the build-up of the laser field. As was pointed out by Lang and Scully, the transmission loss plays the role of an effective noise source, satisfying the fluctuation-dissipation theorem. However, the continuum treatment does not support the mode-locking mechanism, but rather the usual explanation of the laser linewidth in terms of gain narrowing. The nonlinear analysis agrees with the main conclusion of Lang, Scully and Lamb that the ‘mode amplitude’ of the conventional theory should be interpreted as a collective variable that satisfies the well-known rotating-wave Van der Pol oscillator equation. The domain of validity of this result and of the laser quasimode concept depends on an approximation, analogous to the Weisskopf-Wigner approximation, which is well satisfied for the usual case of very long-lived quasimodes.

Optica Acta International Journal of Optics•Jan 1, 1984•31 citations
The rate at which pure initial states satisfying the detailed balance condition on the photon number states deteriorate into mixtures in the decoherence process is computed for a laser field above threshold in the Scully-Lamb laser model. In steady-state laser operation, the field state suggested by Scully and Lamb is shown to be the least increase of the error area in the complex amplitude plane, thus becoming the most stable field state among the squeezed states characterized by the phase order parameter Δ.
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.
Conventional laser theory deals with discrete ‘cavity modes’ and introduces artificial mechanisms to simulate radiation field losses caused by beam extraction. A more realistic model of a laser with a transmitting window, previously investigated by Lang, Scully and Lamb, is reanalysed semiclassically. In the previous work, the continuous radiation field spectrum was treated as the limit of a discrete but very dense spectrum of modes, and the narrowness of the laser linewidth was attributed to the locking together of these modes. Working entirely within the continuous spectrum, we find that the treatment is considerably simplified, leading to an explicit solution for single-quasimode operation within the linear approximation which exhibits the role of the excitation conditions in the build-up of the laser field. As was pointed out by Lang and Scully, the transmission loss plays the role of an effective noise source, satisfying the fluctuation-dissipation theorem. However, the continuum treatment does not support the mode-locking mechanism, but rather the usual explanation of the laser linewidth in terms of gain narrowing. The nonlinear analysis agrees with the main conclusion of Lang, Scully and Lamb that the ‘mode amplitude’ of the conventional theory should be interpreted as a collective variable that satisfies the well-known rotating-wave Van der Pol oscillator equation. The domain of validity of this result and of the laser quasimode concept depends on an approximation, analogous to the Weisskopf-Wigner approximation, which is well satisfied for the usual case of very long-lived quasimodes.