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Physical Review A

Quantum theory of the cold-atom micromaser including gravity

Thierry Bastin, John Martin

Published Nov 22, 2005• 5 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.72.053815

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Acta Physica Sinica•Jan 1, 2001•2 citations
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.
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.
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.
The quantum theory of the cold atom scattering by cavity fields in a two-dimensional geometry is presented. A distinct regime from the usual Raman-Nath, Bragg and Stern-Gerlach regimes is investigated, considering the situation where the cavity light field acts as a repulsive and an attractive two-dimensional potential. General expressions for the scattering lengths (the two-dimensional analogues to the three-dimensional scattering cross-sections) of finding the atoms deexcited or not after their interaction with the cavity are derived. The connection with the classical Rabi limit when the incident atomic kinetic energy is high compared with the atom-field interaction energy is made. In the cold atom regime characterized by much lower incident atomic kinetic energies, the scattering process exhibits very peculiar properties in connection with quasibound states of the atomic motion induced by the attractive potential of the cavity light field.
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.
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).
The effects of the atomic coherence on the photon statistics of the micromaser injected with ultra-cold V-type three-level atoms are studied.In the plot of the atomic emission probability versus the cavity length, there are resonance peaks and non-resonance platforms, which can be adjusted by the atomic coherence parameters.These features of emission probability affect the properties of photon statistics directly. In the plot of the mean number of photons versus the cavity length, there are resonance peaks and non-resonance platforms,too. Given a cavity length, with the change of the atomic coherence parameters, the distribution of photon numbers can move towards the large or small photon numbers, and the mean number of photons increases or decreases accordingly.We also find, with appropriate atomic coherence parameters, that the photon statistics are sub-Poissonian in large region of the cavity length.