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Communications in Theoretical Physics

Quantum Theory of a Nondegenerate Two–Photon Laser

Guojian Yang, Huang Zu-Qia, Gang Xiang Hu

Published Dec 1, 1990• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/14/4/397

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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.
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.
A nondegenerate two-photon laser in a cascade three-level atomic system is studied. The difference between the laser and that derived from an effective Hamiltonian is discussed. Photon number distributions about field 1 are presented. The effects of field 2 on field 1 are studied in detail. Field 2 can play a role of gain enhancement or gain reduction for field 1. This is due to two actions of field 2: reducing the population of the intermediate level and changing the detuning really acting upon field 1, which is caused by the ac Stark shift.
For pt.I see ibid., vol.8, 104 (1974). Investigations into possible multiphoton laser systems are extended to a less restrictive class than considered in the previous paper. The loss mechanism for the light field is now taken to be a single-photon loss. These systems no longer preserve the property of detailed balance. Explicit solutions are given for the stationary photon distribution for the two-photon laser. This exhibits similar photon statistics to the usual one-photon laser, with no significant increase in relative fluctuations at threshold. The results are equally applicable to multiboson lasers involving say the simultaneous stimulated emission of a photon and a phonon.
In this dissertation, we study the quantum theory of two-photon micromaser and laser. To begin with, we study the photon statistics of the two-photon micromaser by considering the interaction of a quantized single-mode field with an effective two-level atom through intermediate states. We present an exact solution for the photon distribution function and study the behaviour of mean photon number and photon number fluctuations. A periodic "collapse" and "revival" type behaviour is predicted. We find that the photon number fluctuations exhibits a periodic sub-Poissonian behaviour with respect to the interaction time. We then discuss the photon statistics of two-photon laser and derive an exact expression for photon distribution function. We find that photon distribution function for two-photon laser is wider than the Poisson distribution function. We also calculate the natural line-width of a two-level two-photon laser by using a Fokker-Planck approach. It is shown that, apart from a constant, the gain contribution to the laser linewidth is equal to the two-photon gain parameter and is independent of the mean number of photons in the field. Finally, we study the two-photon transitions in multi-level atomic system. In this case first we discuss the photon statistics of three-level two-photon micromaser and laser. Then we consider the two-photon transition in four-level atomic system by considering dye laser as an example.
We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with NNN stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.