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arXiv:2205.04428 · Physical Review A

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

Gage W. Harmon, J. Reilly, Murray Holland, Simon B. Jäger

Published Jul 11, 2022• 2 citations
arXivHTMLPDF

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 nonlasing 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 nonlasing solutions that highlight the nonlinear 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.

DOI
10.1103/physreva.106.013706

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Lasing without inversion (LWI) in specific models of closed three-level systems is analyzed in terms of nonlinear dynamics. From a linear stability analysis of the trivial nonlasing solution of the homogeneously broadened systems with on-resonance driving and laser fields, we find that, near lasing threshold, resonant closed $\ensuremath{\Lambda}$ and VVV schemes yield continuous-wave LWI while resonant cascade schemes can give rise to self-pulsing LWI. The origin of this different behavior is discussed. For parameters of a real cascade system in atomic 138Ba{}^{138}\mathrm{Ba}138Ba we check numerically that the self-pulsing solution is stable in a broad range of nonzero detunings. It is shown that the self-pulsing emission can still be observed when the typical residual Doppler broadening of an atomic beam is taken into account.
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