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Physical Review A

Failure of an atomic-injection model for the description of pump fluctuations in masers and lasers

Claus Benkert, Kazimierz Rza̧żewski

Published Feb 1, 1993• 10 citations
Publisher

Abstract

We analyze and discuss the exact solution of a popular model for the influence of pump statistics on laser and maser fields. This model has attracted some attention in recent years and has been used to describe noise reduction in lasers, masers, and micromasers. We show that this model has some serious problems and can create negative probabilities in the photon-number distribution. We determine the origin of the model's deficiency.

DOI
10.1103/physreva.47.1564

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We analyze and discuss the exact solution of a popular model for the influence of pump statistics on laser and maser fields. This model has attracted some attention in recent years and has been used to describe noise reduction in lasers, masers, and micromasers. We show that this model has some serious problems and can create negative probabilities in the photon-number distribution. We determine the origin of the model's deficiency.
We discuss in detail the influence that the statistical properties of the pump source have on maser and laser dynamics. We derive a general master equation for the radiation field that is valid for a wide range of different pump mechanisms. If the pump noise is eliminated, we find that the photon number noise in a micromaser and a laser can be significantly reduced below the shot-noise level. In contrast, the phase fluctuations for both maser and laser are unaffected by the noise contribution of the pump.
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.
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.
We show that regularization of pumping leads to large photon-number noise reduction in one- and two-photon micromasers, and is much more important than in macroscopic lasers and masers. Our calculations are based on a step-by-step microscopic approach and are compared to results obtained from a pumping-statistics-dependent master equation, which is shown not to be entirely reliable in the micromaser case. Although noise reduction and the discrepancies betwen the two approaches are more important for monokinetic beams, they are still relevant when a 10% velocity dispersion is allowed.
We study the one-atom maser with a periodic-pump scheme for the injected atoms. The dynamics of the system is solved also in a regime where the losses of the field cannot be neglected while the atom is inside the cavity, as is the situation in an optical maser. The time development of the maser field is described by a general evolution operator, whose matrix representation in the damping basis is known analytically for zero temperature. The numerical evaluation of this matrix yields the stationary as well as the transient properties of the maser. Noise-producing mechanisms of the pump are included explicitly in the evolution operator for the field. These are a finite efficiency of the pump laser, a velocity spread in the atomic beam, and spontaneous transitions between the atomic levels and to the ground state. We find that features such as trapped states and sub-Poissonian photon statistics also occur in the high-loss regime like in an optical resonator. The observation of such effects will, as in the ordinary micromaser experiments, depend very sensitively on the reduction of the pump noise. For highly regular excitation, we find a pronounced oscillation of the field-correlation function for a wide range of the transit time, which leads to a distinct line splitting in the spectrum of the field. The amount of the splitting is determined by the periodicity of the pump. For less regular excitation, and in particular in the Poissonian limit, these oscillations disappear.