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Journal of Physics B Atomic Molecular and Optical Physics

Quantum theory of the micromaser with ultracold three-level atoms interacting with a bimodal cavity field: spatial variation along the cavity axis

Mahmoud Abdel‐Aty, A.‐S. F. Obada

Published Jul 10, 2003• 3 citations
Publisher

Abstract

The analytical form of the emission probability produced by the interaction of an ultracold three-level atom with an electromagnetic bimodal cavity field with multi-photon transitions of the atoms (multi-photon mazer) is analysed in the framework of the dressed-state formalism, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. In particular, the cavity field mode profile is considered by using the mesa-mode function and differences in the collapse–revival patterns are reported. We demonstrate that, when propagation effects are taken into consideration, the emission probability is influenced significantly. We provide the necessary arguments to justify the validity of our conclusions for emission probability and the micromaser, whose dynamics are governed by the wavefunction. Our main conclusion is that, in the present system, the inclusion of the spatial dependence is necessary and important. The numerical illustrations provide evidence that, in cases of physical interest, the emission probability can be significant and can be reliably estimated for a broad range of field parameters using the present formalism.

DOI
10.1088/0953-4075/36/15/301

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The analytical form of the emission probability produced by the interaction of an ultracold three-level atom with an electromagnetic bimodal cavity field with multi-photon transitions of the atoms (multi-photon mazer) is analysed in the framework of the dressed-state formalism, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. In particular, the cavity field mode profile is considered by using the mesa-mode function and differences in the collapse–revival patterns are reported. We demonstrate that, when propagation effects are taken into consideration, the emission probability is influenced significantly. We provide the necessary arguments to justify the validity of our conclusions for emission probability and the micromaser, whose dynamics are governed by the wavefunction. Our main conclusion is that, in the present system, the inclusion of the spatial dependence is necessary and important. The numerical illustrations provide evidence that, in cases of physical interest, the emission probability can be significant and can be reliably estimated for a broad range of field parameters using the present formalism.
We generalize a study of the behavior of a three-level atom in a single-mode mazer. Our formulation takes into account the interaction region and the spatial variation along the cavity axis. A general analytic time-dependent solution is obtained, and some special cases reduce to very simple expressions. When propagation effects are taken into consideration, the emission probability is influenced significantly. We provide the necessary arguments to justify the validity of our conclusions for emission probability and micromaser whose dynamics is governed by the wave function. Our main conclusion is that in the present system, the inclusion of the spatial dependence of the cavity region is necessary and important. We provide numerous examples to illustrate this correspondence, and provide evidence of its usefulness.
The emission probability of a cold atom in a microcavity when its center-of-mass motion is described quantum mechanically is presented, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. In particular, the mesa mode cavity profile is considered. The quantum theory of the one-photon mazer is constructed in the framework of the dressed-state coordinate formalism. Simple expressions for the atomic populations, the cavity photon statistics, and the reflection and transmission probabilities are given for any initial state of the atom-field system. The general conclusions reached are illustrated by numerical results.
The idea of the two-photon mazer (microwave amplification via z -motion-induced emission of radiation) is put forward. The dressed states for the interaction of a cascade three-level atom with a quantum cavity field are derived. The general quantum theory of the two-photon mazer is established and its emission probability is studied. The effects of the atomic c.m. momentum and of the atom-field detuning are examined. It is found that the two-photon mazer shows new features that differ from both the one-photon mazer and the conventional two-photon micromaser.
We apply the concept of the mazer to the two-photon process and propose the idea of the two-photon mazer. We establish the general quantum theory of the two-photon mazer and calculate its emission probability in the special case of a mesa mode function. We study not only the case in which the cavity field is initially in a number state, but also the case in which the cavity field is initially in a coherent state. Under the condition of an initial coherent field, the emission probability shows the collapse-revival phenomena, which have different features in different regimes. In the thermal-atom regime, the collapse revivals are similar to that in the two-photon Jaynes-Cummings model. In the critical regime, the collapse revivals look like that in the one-photon Jaynes-Cummings model. In the ultracold-atom regime, the collapse revivals are different from those in the above two regimes. The reasons for these results have been analyzed.
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 propose an alternative treatment to describe the spatial-dependence of the non-resonant two-photon mazer. Previous work presented a treatment for studying the cold atom micromaser (mazer) but under certain restrictive conditions. We now extend those results to a general case taking into account the spatial dependence, off-resonant interaction and Stark-shift. In a mesa mode profile, we obtain an exactly analytic solution of the model, by means of which we analyze the analytical form of the emission probability. We demonstrate that, when the spatial dependence effects are taken into consideration, the feature of the emission probability is influenced significantly.