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Optica Acta International Journal of Optics

Photon Statistics for a Laser with Intracavity Two-photon Absorption

G. P. Hildred

Published Dec 1, 1980• 10 citations
Publisher

Abstract

The quantum statistical properties of light produced by a laser below threshold with intracavity two-photon absorption are reconsidered. In contradistinction to the work of previous authors, antibunching is predicted. A method for converting photon rate equations into differential equations for intensity autocorrelation functions is also presented.

DOI
10.1080/713820184

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The quantum statistical properties of light produced by a laser below threshold with intracavity two-photon absorption are reconsidered. In contradistinction to the work of previous authors, antibunching is predicted. A method for converting photon rate equations into differential equations for intensity autocorrelation functions is also presented.
A model of two photon absorption in a cavity with an external driving field is presented. Phase and amplitude fluctuations in the driving field are taken into account to model a partially coherent multimode source. The photon statistics of the light in the cavity are investigated through a calculation of the second-order correlation function of the light field in the steady state. For a coherent driving field the field inside the cavity will exhibit photon antibunching for low intensities. As the fluctuations in the driving field are increased the photon antibunching is lost. For a particular coherent field, g (2) (0) is reduced with increasing laser intensity. This reduction with laser intensity is slower with increasing laser amplitude fluctuations. This could provide a possible explanation for the recent experimental observations of Kransinski and Dinev (1976).
A theory of a quantum amplifier based on two-photon transitions is presented. The model consists of an assemblage of atoms interacting with a single mode of the light field via two-photon absorption and emission. The treatment is quantum mechanical, and the emphasis is on the photon-statistical aspects of the problem. Difference-differential equations for the density matrix of the field mode are derived. The equations are solved for a special case. Differential equations for the expectation vaues of the number of photons and of the field amplitudes, and for their higher statistical moments, are also obtained. Approximate solutions for the average number of photons are found, and the effect of the amplification process on the statistical fluctuations of the number of photons and the field amplitudes is discussed. The results of this study suggest that such an amplifier does not have the coherence properties of a laser amplifier because it tends to increase the statistical fluctuations of the field.
This paper presents a theoretical analysis of the optical properties of an optical cavity with both one- and two-photon intracavity absorption loss, without saturation. The cavity two-photon absorption loss per pass is assumed to be small, but otherwise the analysis is general. Analytical results for the cavity transmission as a function of cavity parameters, linear and two-photon intracavity loss, and detuning from resonance are derived and limiting cases discussed. Extraction of the two-photon loss from both cavity ring-down and cavity-enhanced absorption spectroscopy methods is analyzed and the predicted shot-noise limited sensitivities derived and compared. Numerical results are computed using the parameters of a recent experimental intracavity measurement of two-photon absorption of nitrous oxide. The results will be useful in the design and interpretation of cavity-enhanced, two-photon absorption spectroscopy.
We have measured the second-order correlation function of the cavity-QED microlaser output and observed a transition from photon bunching to antibunching with increasing average number of intracavity atoms. The observed correlation times and the transition from super- to sub-Poisson photon statistics can be well described by gain-loss feedback or enhanced-reduced restoring action against fluctuations in photon number in the context of a quantum microlaser theory and a photon rate equation picture. However, the theory predicts a degree of antibunching several times larger than that observed, which may indicate the inadequacy of its treatment of atomic velocity distributions.
It has been widely accepted that the conventional lasing threshold, occurring around unity intracavity photon number, can be eliminated by making the so-called β\betaβ parameter approach unity. Recently, it has been shown that the photon statistics become incoherent when the intracavity mean photon number is decreased below unity even for β≈1\beta \approx 1β≈1. Here, we report systematic measurement of the photon statistics in a superradiant laser as a function of the intracavity photon number. Our superradiant laser was based on the single-atom superradiance driven by twolevel atoms in a quantum superposition state traversing a high-Q cavity one by one. The lasing did not exhibit the conventional threshold and the photon statistics remained near coherent even well below unity photon number. Moreover, the coherence got better as the excited-state population in the initial superposition state was made smaller.