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arXiv:quant-ph/0505133 · Journal of Physics B Atomic Molecular and Optical Physics

Comment on Quantum inversion of cold atoms in a microcavity: spatial dependence

Thierry Bastin, J Martin

Published Oct 8, 2003• 2 citations
arXivHTMLPDF

Abstract

In a recent work, Abdel-Aty and Obada ( 2002 J. Phys. B: At. Mol. Opt. Phys. 35 807–13 ) analysed the quantum inversion of cold atoms in a microcavity, the motion of the atoms being described quantum mechanically. Two-level atoms were assumed to interact with a single mode of the cavity, and the off-resonance case was considered (namely the atomic transition frequency is detuned from the single-mode cavity frequency). We demonstrate in this paper that this case is incorrectly treated by these authors, and we therefore question their conclusions.

DOI
10.1088/0953-4075/36/20/n01

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In a recent work, Abdel-Aty and Obada ( 2002 J. Phys. B: At. Mol. Opt. Phys. 35 807–13 ) analysed the quantum inversion of cold atoms in a microcavity, the motion of the atoms being described quantum mechanically. Two-level atoms were assumed to interact with a single mode of the cavity, and the off-resonance case was considered (namely the atomic transition frequency is detuned from the single-mode cavity frequency). We demonstrate in this paper that this case is incorrectly treated by these authors, and we therefore question their conclusions.
In a recent work, Abdel-Aty and Obada [2002 J. Phys. B 35 807-813] analyzed the quantum inversion of cold atoms in a microcavity, the motion of the atoms being described quantum mechanically. Two-level atoms were assumed to interact with a single mode of the cavity, and the off-resonance case was considered (namely the atomic transition frequency is detuned from the single mode cavity frequency). We demonstrate in this paper that this case is incorrectly treated by these authors and we question therefore their conclusions.
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.
We study quantum inversion of a cold atom in the Jaynes-Cummings model when its centre-of-mass (CM) motion is described quantum mechanically. The atom and the quantized cavity mode are initially prepared in the excited state and the coherent state, respectively. Many dramatic changes take place in atomic inversion when the atomic CM motion experiences a transition from the classical regime to the quantum regime. For ultra-cold atoms, in particular, fine resonances are found in the inversion. This novel effect, which originates from the de Broglie wave character of the atomic CM motion, is a direct manifestation of the `granularity' of the high-intensity cavity field. By means of the atom-field dressed-state picture, we explain the related phenomena in a qualitative way.
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 quantum theory of the cold atom micromaser including the effects of gravity is established in the general case where the cavity mode and the atomic transition frequencies are detuned. We show that atoms which classically would not reach the interaction region are able to emit a photon inside the cavity. The system turns out to be extremely sensitive to the detuning and in particular to its sign. A method to solve the equations of motion for non resonant atom-field interaction and arbitrary cavity modes is presented.