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Modern Physics Letters B

INDUCED EMISSION OF COLD ATOMS PASSING THROUGH A MICROMASER CAVITY: SPATIAL DEPENDENCE

Mahmoud Abdel‐Aty, A.‐S. F. Obada

Published Feb 20, 2002• 9 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984902003580

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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 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 atomic inversion of cold atoms in a microcavity when its centre-of-mass (CM) motion is described quantum mechanically is presented, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. It is shown that the spatial dependence of the atomic inversion is very sensitive to changes of the atomic CM motion, as well as the cavity length. For ultracold atoms, different behaviours in the atomic inversion are demonstrated for the change in cavity length. The general conclusions reached are illustrated by numerical results.
The photon emission probability in a micromaser changes drastically when the kinetic energy of the pumping atoms is comparable to the atom-field interaction energy. In this situation, the atomic center-of-mass motion has to be treated quantum mechanically and the de Broglie wavelength of the atom inside the cavity is an important physical parameter. The interplay between reflection and transmission of the atoms leads to a new mechanism for induced emission. A photon is emitted by an excited atom when the de Broglie wavelength fits resonantly into the cavity. These resonances lead to the process of microwave amplification via zzz-motion-induced emission of radiation (mazer). We derive and illustrate a general expression for the emission probability and a master equation for the mazer. We note that the probability for emission by an excited thermal atom (stimulated maser emission) is very different from the emission probability as given by the de Broglie resonances (induced mazer emission).
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.
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.