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Journal of Optics B Quantum and Semiclassical Optics

Co-operative atomic interactions in one- and two-photon micromasers

I Ashraf, A. H. Toor

Published Nov 21, 2000• 6 citations
Publisher

Abstract

We have developed a quantum theory of the micromaser for a pair of two-level atoms for the case of one- and two-photon transition coupling. We have studied the effect of co-operativity on the photon statistics for these systems for different coupling constant ratios. It is found that for equal coupling, our system of a two-atom, one-photon micromaser behaves like a double one-photon cascade micromaser. Similarly, for equal coupling, the photon statistics of the two-atom, two-photon micromaser reduces to that of a three-level, four-photon cascade micromaser.

DOI
10.1088/1464-4266/2/6/309

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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 derive the dressed states for the interaction of a cascade three-level atom with a quantum cavity field, suggest using ultra-cold cascade three-level atoms in micromasers, put forward the idea of the two-photon mazer, establish its general quantum theory and study its emission probability and photon statistics. We examine the effects of the atomic centre-of-mass momentum, the atom-field detuning, the photon number in thermal equilibrium, the ratio of the atomic injection rate to the cavity decay rate and the interaction length on the emission probability and the photon statistics.
We have investigated the steady-state cavity-field properties of a single-mode two-photon micromaser when the atoms in a cascade three-level configuration are initially prepared in a mixture of the upper and intermediate states. The mean photon number, trapping state and sub-Poissonian effect are discussed with upper (intermediate)-state population changing from 1(0) to 0(1). These properties are very different from those in a pure two- or one-photon transition process, due to the competition among different transition processes. In particular, the trapping states of nonzero photons are discovered in this system under some conditions, which is contrary to the previous findings.
We present the quantum theory of the two-mode micromaser operating on \ensuremath{\Lambda}-type three-level atoms. The explicit expression of the detailed-balance steady-state photon distribution is derived. The photon statistics and the correlation between the modes are studied. It is shown that due to the strong anticorrelation between the modes the fluctuations in the total number of photons may be sub-Poissonian even when the fluctuations in the number of photons in each mode are super-Poissonian.
The authors develop the theory of the degenerate and nondegenerate two-photon micromaser using the full, three-level Hamiltonian under conditions of overall two-photon resonance. Subject to this condition, their results are valid for arbitrary one-photon detunings, but they consider in particular the large detuning and zero detuning limits, where some simplification is possible. For the case of zero detuning, they obtain semianalytic solutions, and find that, depending upon the interaction time, the system lases as either a single-mode or a two-mode system. They have compared their results with the degenerate two-photon micromaser, and find qualitative differences. Their results are valid for arbitrary one-photon detunings, provided the interaction times are not too long. The solution to the Fokker-Planck equation is found using a detailed balance, linearization procedure, and the photon statistics is investigated. Markedly sub-Poissonian behaviour is possible under certain conditions. They find that the behaviour in the zero detuning, nondegenerate situation is quite distinct to that of all other cases.