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arXiv:quant-ph/0412043 · Physical Review A

Detuning effects in the one-photon mazer

Thierry Bastin, John Martin

Published May 27, 2003• 27 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.67.053804

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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.
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)].
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.
A theoretical approach is proposed to deal with the detuning between the atom and cavity field in the one-photon mazer. Our starting point is to find a conserved quantity, which is characteristic of the atom plus field system. Resorting to this characteristic conserved quantity, we separate the Hamiltonian into two independent parts and then solve the Schr6dinger equation of quantum scattering of an incident cold atom. We investigate the detuning effects on the one-photon induced emission probability and obtain some distinct results in contrast to the previous work.
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).
A theoretical approach is proposed to deal with the detuning between the atom and cavity field in the one-photon mazer. Our starting point is to find a conserved quantity, which is characteristic of the atom plus field system. Resorting to this characteristic conserved quantity, we separate the Hamiltonian into two independent parts and then solve the Schrödinger equation of quantum scattering of an incident cold atom. We investigate the detuning effects on the one-photon induced emission probability and obtain some distinct results in contrast to the previous work.
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.