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arXiv · 2205.04428

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

Gage W. Harmon·Jarrod T. Reilly·Murray J. Holland·Simon B. Jäger
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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.

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Gage W. Harmon, Jarrod T. Reilly, Murray J. Holland, Simon B. Jäger. 2022-05-09. Mean-field Floquet theory for a three-level cold-atom laser. https://doi.org/10.1103/physreva.106.013706

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