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Physical Review A

Effect of atomic decay on micromasers

Shi-Yao Zhu, L. Z. Wang, H. Fearn

Published Jul 1, 1991• 18 citations
Publisher

Abstract

The decay of the active atoms in micromasers is theoretically analyzed. The equations of motion for the diagonal elements of the micromaser field, which include an atomic-decay effect, have been obtained. The relation between the photon statistics and the micromaser field on the atomic decay has been studied. The effect of atomic-decay rates and average photon numbers, photon-number variances, and the photon-number distribution has been discussed. It has been shown that generation of approximate trapping states or number states requires very small atomic-decay rates and very large field-atom coupling constants.

DOI
10.1103/physreva.44.737

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Physical Review A•Apr 1, 1991•9 citations
The decay of the active atoms in micromasers is theoretically analyzed. The equations of motion for the diagonal elements of the micromaser field, which include an atomic-decay effect, have been obtained. The relation between the photon statistics and the micromaser field on the atomic decay has been studied. The effect of atomic-decay rates and average photon numbers, photon-number variances, and the photon-number distribution has been discussed. It has been shown that generation of approximate trapping states or number states requires very small atomic-decay rates and very large field-atom coupling constants.
The lifetimes of Rydberg atoms have been considered in micromaser theory. The difference from the usual micromaser theory [P. Filipowicz, J. Javanainen, and P. Meystre, Phys. Rev. A 34, 3077 (1986)] without level decay rates is discussed. It is shown that when the atom-field interaction time is large, the quantum collapse and revival are significantly different from the prediction of the usual micromaser theory. The relation between the photon fluctuation and the fluctuation of the population of the lower level after interacting with a maser field is also discussed. We found that the consistency of the sub-Poisson statistics of the lower-level population and photon number is violated.
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.
We have established the master equation for the micromaser with a Kerr medium. We have studied the photon statistics of the micromaser with a Kerr medium field and analysed the influence of the Kerr effect on the photon statistics. The influence of the Kerr effect on the photon statistics is different in two regimes. In the thermal-atom regime, the Kerr effect produces quantum noise and decreases the mean photon number. In the ultracold-atom regime, with the increase of the nonlinear parameter of the Kerr medium, the stability of the mean photon number and the normalized variance enhances the mean photon number and the normalized variance exhibits collapse-revival phenomena periodically, their resonance peaks become lower and the photon statistics of more and more regions are sub-Poissonian.
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.