Quantum-limited phase-matching effect in aΛ-type laser system

Abstract

The theory of a quantum-limited phase-matching effect in a $\ensuremath{\Lambda}$-type lasing system is studied in detail based on the quantum Langevin approach. Two quasimonochromatic fields are directly generated based on two lasing transitions. We find that the coherence between two lasers can well exceed the linewidth of either laser field. This result denotes that two field phases match each other although either laser field has a high phase fluctuation. Unlike the phase-matching effect based on atomic absorption, the final coherence between two laser fields here is not limited by saturation broadening, and the higher laser intensities lead to a higher coherence. Additionally, based on a linear stability analysis, we find that the instability of the field steady state can substantially restrict the occurrence of this phase-matching effect in the bad-cavity limit for a high pump rate. We also discuss the spectrum of amplitude fluctuations of output fields, and the result shows that the squeezing of amplitude fluctuations at low frequencies for a single field oscillating inside the cavity is damaged in the case of two fields oscillating.