Self-Organization Threshold with an External Potential

TL;DR

This paper derives threshold conditions for laser-driven atomic self-organization in optical cavities, considering different probing schemes and the influence of intra-cavity trapping potentials, providing a comprehensive theoretical framework.

Contribution

It introduces a unified theoretical derivation of self-organization thresholds accounting for various probing geometries and intra-cavity potentials, expanding previous models.

Findings

Threshold equations depend on probe configuration and cavity detuning.

Intra-cavity trapping potentials significantly affect the self-organization threshold.

Different probing schemes lead to qualitatively different system responses.

Abstract

We derive threshold equations for self-organization of laser driven atoms in an optical cavity. Our analysis includes probing with either a traveling wave or a retro reflected lattice. These two scenarios lead to qualitatively different behavior in terms of the response of the system as a function of cavity detuning with respect to the probe. In addition our analysis includes the effects of an intra-cavity trapping potential which is also shown to impact on the threshold condition. We specifically consider the case of an intra-cavity lattice but our treatment can easily be modified to other geometries.