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Journal of Optics B Quantum and Semiclassical Optics

The influence of atomic decay on the linewidth of a two-photon micromaser

M Y Hamza, Shahid Qamar

Published Jun 1, 2000• 5 citations
Publisher

Abstract

In this paper, we study the influence of atomic decay on the linewidth of a two-photon micromaser using an exact Hamiltonian approach. We consider a three-level cascade atomic system (where each level has a finite lifetime) interacting with a single mode of the radiation field. The intermediate level is considered to be off resonant with the field. We calculate the linewidth for both small- and large-detuning limits. In both cases, the well known oscillatory behaviour of the linewidth vanishes for large decay rates. We also find a reduction in the linewidth in certain regions of interaction times. In the limit of small decay rates, we recover the linewidth of the ordinary two-photon micromaser. We also compare the results under the large-detuning limit with the results obtained using a phenomenological Hamiltonian approach.

DOI
10.1088/1464-4266/2/3/316

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Journal of Physics B Atomic Molecular and Optical Physics•May 26, 2000•9 citations
In this paper, we study the influence of atomic decay on the linewidth of a two-photon micromaser using an exact Hamiltonian approach. We consider a three-level cascade atomic system (where each level has a finite lifetime) interacting with a single mode of the radiation field. The intermediate level is considered to be off resonant with the field. We calculate the linewidth for both small- and large-detuning limits. In both cases, the well known oscillatory behaviour of the linewidth vanishes for large decay rates. We also find a reduction in the linewidth in certain regions of interaction times. In the limit of small decay rates, we recover the linewidth of the ordinary two-photon micromaser. We also compare the results under the large-detuning limit with the results obtained using a phenomenological Hamiltonian approach.
In this paper, we study the linewidth of a two-photon micromaser by using an exact Hamiltonian approach. We consider a three-level atomic system interacting with a single-mode radiation field. The intermediate level is considered to be off resonant with the field. In this model, under the large detuning limit, two-photon transitions result. We calculate the linewidth of a two-photon micromaser and present results in the small and large detuning limits. In the small detuning limit, single-photon behavior is evident, whereas in the large detuning limit, true two-photon behavior is exhibited. We compare the results for the linewidth, under a large detuning limit, with the results obtained by using a phenomenological, effective Hamiltonian approach. The absence of the dynamic Stark shift in a phenomenological, effective Hamiltonian leads to qualitatively different results in the two approaches. \textcopyright{} 1996 The American Physical Society.
We study degenerate two-photon micromasers pumped by cascade three-level atoms, where each atomic energy level has a different linewidth. Our model allows us to recover the ordinary two-photon micromaser situation when these widths vanish. In the limit of large linewidths we obtain a two-photon laser model. We show that trapping states are extremely sensitive to atomic decay, even when the decay time is small in comparison to the transit time through the cavity. Unlike the one-photon micromaser, they are sensitive to the linewidth of the upper, as well as the lower energy level. We have also studied the effects of atomic decay on the starting time of micromasers and on the noise. We found that there is a significant difference between the behavior of two-photon micromasers and lasers as we change the ratio of the widths of the upper and lower levels.
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.
Exact results for the photon statistics of a two-photon micromaser are presented, including the effect of finite detuning of the intermediate level. A periodic dependence on interaction times is shown to arise for large detunings, when sufficiently long interaction times are considered. Some typical photon-number distributions are shown, including some exhibiting sub-Poissonian fluctuations and multiple peaks. Previous treatments and the validity of some usual approximations are discussed. By direct comparison with the exact results, it is shown that the effective-Hamiltonian approximation yields incorrect equations for the off-diagonal elements of the field density matrix.
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 study the spectrum of the micromaser injected with ultracold cascade three-level atoms. We examine the effects of the atomic centre-of-mass motion, the cavity length, the atom-field detuning, the ratio of the atomic injection rate to the cavity decay rate, and the number of photons in thermal equilibrium on the spectrum. We find that the micromaser injected with ultracold three-level atoms shows new spectral properties which are different from those of the micromaser injected with ultracold two-level atoms and the micromaser injected with thermal two- or three-level atoms. The main conclusions are that the linewidth can be broadened and the frequency can be either red-shifted or blue-shifted.