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Detuning effects in the vertical cold atom micromaser

John Martin, Thierry Bastin

Published Jan 1, 2006• 1 citation
OpenAlex

Abstract

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.

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A short review of the theoretical studies of the cold atom micromaser (mazer) is presented. Existing models are then improved by considering more general working conditions. Especially, the mazer physics is investigated in the situation where a detuning between the cavity mode and the atomic transition frequency is present. Interesting new effects are pointed out. Especially, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. The transmission probability of ultracold atoms through a micromaser is also studied and we generalize previous results established in the resonant case. In particular, it is shown that the velocity selection of cold atoms passing through the micromaser can be very easily tuned and enhanced using a nonresonant field inside the cavity. This manuscript is a summary of Martin's master thesis and articles [Phys. Rev. A 67, 053804 (2003)] and [Eur. Phys. J. D 29, 133 (2004)].

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

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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.

arXiv:quant-ph/0505133•Journal of Physics B Atomic Molecular and Optical Physics•Oct 8, 2003•2 citations
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.
The quantum theory of the cold-atom micromaser including the effects of gravity is considered. We show that gravity does not break the special properties of the induced emission probability for the micromaser in the cold atom regime and rather new effects are predicted. In particular, we show that the cavity acts in the gravity field as an additional repulsive and attractive potential, resulting in quasibound states of the atomic motion. This feature gives rise to fine resonances in the induced emission probability that are not restricted to any particular cavity mode function, in contrast to the usual cold-atom micromaser. It is also shown that the atom is able to emit a photon inside the cavity, though classically it does not reach the interaction region. Predictions about the photon number statistics when the cavity is pumped by a flux of excited atoms are finally given. Unusual highly nonclassical ``dragon'' distributions are still predicted in the vertical geometry.
We analyze the quantum theory of the two-mode micromaser pumped by cold three-level atoms with a $\ensuremath{\Lambda}$-configuration under the two-photon resonance condition. We focus more specifically on the large detuning limit where the detuning between the two cavity mode frequencies and the two atomic transition frequencies is large in comparison with the atom-cavity coupling constants. We show that this regime can mimic a virtual two-level atom micromaser without spontaneous emission where the cavity acts for the atoms as a potential barrier or a potential well (depending on the sign of the detuning) and a zero potential but no more both as a potential barrier and a potential well as it is the case for the usual cold two-level atom micromaser [M. O. Scully, G. M. Meyer, and H. Walther, Phys. Rev. Lett. 76, 4144 (1996)]. This introduces interesting options for engineering the interaction between the cold atoms and the cavity. The elimination of the spontaneous emission solves a major issue of the conventional cold two-level atom micromaser as the transit time of cold atoms inside and in the vicinity of the cavity is usually much larger than the atomic level lifetimes. It is also shown that the cold atom regime is very sensitive to the sign of the detuning (in contrast to the hot atom regime) and that, according to this sign, the cavity may speed up or slow down the incident three-level atoms after their interaction with the field.
A short review of the theoretical studies of the cold atom micromaser (mazer) is presented. Existing models are then improved by considering more general working conditions. Especially, the mazer physics is investigated in the situation where a detuning between the cavity mode and the atomic transition frequency is present. Interesting new effects are pointed out. Especially, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. The transmission probability of ultracold atoms through a micromaser is also studied and we generalize previous results established in the resonant case. In particular, it is shown that the velocity selection of cold atoms passing through the micromaser can be very easily tuned and enhanced using a nonresonant field inside the cavity. This manuscript is a summary of Martin's master thesis and articles [Phys. Rev. A 67, 053804 (2003)] and [Eur. Phys. J. D 29, 133 (2004)].
The quantum theory of the mazer in the nonresonant case (a detuning between the cavity mode and the atomic transition frequencies is present) is described. The generalization from the resonant case is far from being direct. Interesting effects of the mazer physics are pointed out. In particular, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. It is also shown that the detuning adds a potential step effect not present at resonance and that the use of positive detunings defines a well-controlled cooling mechanism. In the special case of a mesa cavity mode function, generalized expressions for the reflection and transmission coefficients have been obtained. The general properties of the induced emission probability are finally discussed in the hot, intermediate, and cold atom regimes. Comparison with the resonant case is given.
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.
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.