Mean-field Floquet theory for a three-level cold-atom laser

TL;DR

This paper develops a mean-field Floquet theory for a three-level cold-atom laser in a V-configuration, revealing lasing mechanisms, symmetry breaking, bistability, and hysteresis, and compares it with a cumulant approach.

Contribution

It introduces a mean-field Floquet method to analyze lasing in a three-level atom system, capturing non-linear dynamics and bistability.

Findings

Lasing threshold and frequency determined by stability analysis.

Lasing involves breaking of a continuous U(1) symmetry.

Bistability and hysteresis observed in the system.

Abstract

We present a theoretical description for a lasing scheme for atoms with three internal levels in a $V$-configuration and interacting with an optical cavity. The use of a $V$-level system allows for an efficient closed lasing cycle to be sustained on a dipole-forbidden transition without the need for incoherent repumping. This is made possible by utilizing an additional dipole-allowed transition. We determine the lasing threshold and emission frequency by performing a stability analysis of the non-lasing solution. In the lasing regime, we use a mean-field Floquet method (MFFM) to calculate the lasing intensity and emission frequency. This MFFM predicts the lasing transition to be accompanied by the breaking of a continuous $U(1)$ symmetry in a single Fourier component of the total field. In addition, we use the MFFM to derive bistable lasing and non-lasing solutions that highlight the non-linear nature of this system. We then test the bistability by studying hysteresis when slowly ramping external parameters across the threshold and back. Furthermore, we also compare our mean-field results to a second-order cumulant approach. The work provides simple methods for understanding complex physics that occur in cold atom lasers with narrow line transitions.