### Abstract

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 language | English |
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Article number | 011108 |

Number of pages | 13 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 78 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 2008 |

### Keywords

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

### Cite this

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*,

*78*(1), [011108]. https://doi.org/10.1103/PhysRevE.78.011108