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Physical Review A

Quantum theory of an inhomogeneously broadened two-photon laser

N. Nayak, B. K. Mohanty

Published Mar 1, 1979• 58 citations
Publisher

Abstract

A quantum statistical analysis of a two-photon laser is presented in a generalization of the one-photon laser. A two-photon loss mechanism is assumed by taking detailed-balance considerations into account. The expressions for the photon statistical distribution exhibit the exact influence of the Doppler parameter and other relaxation parameters. In addition, the photon statistics can be studied as a function of the detuning. Threshold conditions for the laser action are noticed. The peak photon number and half-width of the photon distributions are obtained. It is found that the photon distribution can be written as a ratio of the one-photon laser-photon distribution to the Poisson distribution for photons.

DOI
10.1103/physreva.19.1204

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We generalize Lamb's quantum theory of lasers to treat the off-resonance operation of two-transition lasers in inhomogeneously broadened media. The master equation is derived from the density-matrix equation of motion in the Doppler limit. We first find the stationary-state solution from which we then obtain such operation characteristics as the threshold condition, the mean photon number, and the half-width of photon distribution. Compared with the one-transition laser, it is found that in the two-transition laser it is much easier to start oscillation and to obtain higher gain. Furthermore, we find that the two-transition laser is less sensitive to the detuning effect and its deviation from the coherent state is smaller than that of the one-transition laser. The remarkably different hole-burning phenomenon is also discussed.

Physical Review A•Sep 1, 1988•1 citation
A quantum statistical analysis of a two-photon laser is presented in a generalization of the one-photon laser. A two-photon loss mechanism is assumed by taking detailed-balance considerations into account. The expressions for the photon statistical distribution exhibit the exact influence of the Doppler parameter and other relaxation parameters. In addition, the photon statistics can be studied as a function of the detuning. Threshold conditions for the laser action are noticed. The peak photon number and half-width of the photon distributions are obtained. It is found that the photon distribution can be written as a ratio of the one-photon laser-photon distribution to the Poisson distribution for photons.
A quantum-statistical analysis of multi-photon lasers including the effect of detuning and atomic motion is presented. The equations are solved to fourth order in the atom-field coupling constant. Systems in detailed balance (with multi-photon loss mechanism) as well as systems without detailed balance (with single-photon loss mechanism) are considered separately. Treatments for the single-mode and multi-mode processes are given. Expressions for threshold conditions, peak photon number and the half width of photon distribution are obtained. The variation of mean output photon number, the effect of detuning, the coherence characteristics, etc. are studied and results are illustrated for two- and three-photon lasers as examples.
The results of the quantum theory of a laser given by Riska and Stenholm (see ibid., vol.3, p.536 (1970)) for the case of inhomogeneous broadening and detuning are re-derived by avoiding the Doppler limit approximation to show the exact influence of relaxation parameters on the theory. The threshold condition is seen to be dependent on gamma ab /ku where gamma ab is the relaxation parameter and ku the Doppler parameter. Its value is found to be higher than earlier results. It is noted that the photon distribution function at resonance is much closer to the corresponding distribution obtained from exact calculations for the tuned case. The photon number at the peak of the distribution curve is much lower than earlier values for comparable situations.
Laser actions and photon statistics for a nondegenerate two–photon laser in an effective three–level atomic system with arbitrary detuning are investigated both semiclassically and quantum mechanically, Due to the two–photon effect, the radiation field easily displays a sub–Foissonlan statistical distribution. The laser actions for a two–photon and a single–photon loss mechanisms are compared. It Is found that the detailed balance in the single–photon loss mechanism can still be preserved in the case that a first–order phase transtion takes place.
The results of the Riska-Stenholm quantum theory for an inhomogeneously broadened laser are re-derived without using the Doppler limit approximation which restricts the utility of this theory. The photon distribution peak is seen to occur at a significantly lower photon number and the threshold condition is dependent on Yablku, where Yab is the relaxation parameter and ku the Doppler parameter. The dimensionless intensity parameter is obtained and the results are compared with the existing theories of Riska and Stenholm and of Scully and Lamb.
A quantum-mechanical model for a multiphoton laser is proposed by an obvious generalization of the usual one-photon laser model. The authors consider a class of lasers which preserve detailed balance. This condition is ensured by assuming a multiphoton loss mechanism for the laser light of the same order as the multiphoton gain from the stimulated emission process. Solutions for the stationary density operator of the light field are obtained by a straightforward generalization of the techniques of Scully and Lamb. The multiphoton laser around threshold exhibits behaviour analogous to a second-order phase transition. A non-thermal distribution of multiphoton laser light is achieved above threshold.
We generalize Lamb's quantum theory of lasers to treat the off-resonance operation of two-transition lasers in inhomogeneously broadened media. The master equation is derived from the density-matrix equation of motion in the Doppler limit. We first find the stationary-state solution from which we then obtain such operation characteristics as the threshold condition, the mean photon number, and the half-width of photon distribution. Compared with the one-transition laser, it is found that in the two-transition laser it is much easier to start oscillation and to obtain higher gain. Furthermore, we find that the two-transition laser is less sensitive to the detuning effect and its deviation from the coherent state is smaller than that of the one-transition laser. The remarkably different hole-burning phenomenon is also discussed.