Collective atomic recoil laser as a synchronization transition

J. Javaloyes, M. Perrin, A. Politi

Research output: Contribution to journalArticlepeer-review

69 Citations (Scopus)


We consider here a model previously introduced to describe the collective behavior of an ensemble of cold atoms interacting with a coherent electromagnetic field. The atomic motion along the self-generated spatially periodic force field can be interpreted as the rotation of a phase oscillator. This suggests a relationship with synchronization transitions occurring in globally coupled rotators. In fact, we show that whenever the field dynamics can be adiabatically eliminated, the model reduces to a self-consistent equation for the probability distribution of the atomic "phases." In this limit, there exists a formal equivalence with the Kuramoto model, though with important differences in the self-consistency conditions. Depending on the field-cavity detuning, we show that the onset of synchronized behavior may occur through either a first- or second-order phase transition. Furthermore, we find a secondary threshold, above which a periodic self-pulsing regime sets in, that is immediately followed by the unlocking of the forward-field frequency. At yet higher, but still experimentally meaningful, input intensities, irregular, chaotic oscillations may eventually appear. Finally, we derive a simpler model, involving only five scalar variables, which is able to reproduce the entire phenomenology exhibited by the original model.

Original languageEnglish
Article number011108
Number of pages13
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number1
Publication statusPublished - Jul 2008


  • pulse-coupled oscillators
  • 2-level atoms
  • gain
  • populations
  • radiation
  • networks
  • states
  • vapor


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