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.
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.
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.
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.
The statistics of the beam of excited atoms that pumps a micromaser influence the photon number distribution of the cavity field. Of the cases studied so far, regular injection statistics minimize the number fluctuations and Poisson statistics maximize them. Here we extend these studies in two directions. Previous master equations describing sub-Poissonian injection statistics were derived by using standard reservoir theory. Recently, corrections to these equations have been found that involve the commutator of the gain and loss operators. Describing the system by a discrete map, we can avoid the approximations inherent in reservoir theory. The results are compared to those of the master equation. Differences are found to be small for large photon number but increasingly important for decreasing photon number and pump beam intensity, indicating the breakdown of reservoir theory in this regime. We give an approximate expression for the photon number distribution for weak damping and discuss its connection with semiclassical theory. Finally, we generalize our treatment for super-Poissonian pump fluctuations.
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.
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.
We present a theory of the micromaser including the effect of the arrival-time statistics of the active atoms in the theoretical treatments. Our starting point is an approach that explicitly incorporates the effect of pump statistics into the dynamical description of lasers and masers. We show that the application of standard laser theory to the micromaser is tantamount to the tacit assumption of Poissonian arrival-time statistics. Hence standard laser theory and the theory of the micromaser are, in general, not equivalent, but the latter contains the former, as a limiting case, for completely random arrival times. We show, as an application, that the steady-state value of the average photon number (first moment) is essentially unaffected by the pump statistics since it depends only on the flux of active atoms (average number of atoms entering the cavity per unit time) provided the flux is constant. The intensity fluctuations (second moment), however, exhibit a stronger dependence on the pump statistics. In particular, for sub-Poissonian pump statistics the sub-Poissonian character of the field is enhanced.