Collective Atomic Recoil Laser as a synchronization transition

TL;DR

This paper models a collective atomic recoil laser as a synchronization transition, revealing phase transition behaviors, bifurcations, and chaos, with a simplified model capturing the phenomena.

Contribution

It establishes a formal link between atomic recoil laser dynamics and synchronization models like Kuramoto, identifying phase transitions and chaotic regimes.

Findings

Synchronization can occur via first- or second-order phase transitions.

A secondary threshold leads to self-pulsing and frequency unlocking.

Chaotic oscillations may emerge at high input intensities.

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.