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Journal of Physics B Atomic Molecular and Optical Physics

Emission probability and photon statistics of a coherently driven mazer

Jin Xiong, Zhi‐Ming Zhang

Published Apr 24, 2002• 5 citations
Publisher

Abstract

The idea of a mazer is put forward with particular reference to the question of the driving-induced atomic coherence, which is established by a coherent driving field. The interaction of a quantum cavity field and an ultracold V-type three-level atom in which two levels are coupled by a coherent driving field, is derived. Its general quantum theory is established and the atomic emission probability and photon statistics are calculated and analysed. It is found that the mazer based on this driving-induced atomic coherence shows new features. There is a non-vanishing probability for the atom emitting a photon in the cavity even when the resonance condition is not fulfilled (here the resonance condition means that the cavity length is an integer multiple of half the atomic de Broglie wavelength). Under the resonance condition, the atomic emission probability has two sets of resonance peaks. For a very strong coherent driving field, the emission of the atom can be forbidden. As to the photon statistics, when the driving field is not very strong, the driving-induced atomic coherence reduces the photon number fluctuations of the cavity field. The photon statistics exhibits strong sub-Poissonian behaviour. In the region considered here, it can even be sub-Poissonian for any cavity length. However, when the driving field is too strong, the sub-Poissonian property may disappear.

DOI
10.1088/0953-4075/35/9/313

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The idea of a mazer is put forward with particular reference to the question of the driving-induced atomic coherence, which is established by a coherent driving field. The interaction of a quantum cavity field and an ultracold V-type three-level atom in which two levels are coupled by a coherent driving field, is derived. Its general quantum theory is established and the atomic emission probability and photon statistics are calculated and analysed. It is found that the mazer based on this driving-induced atomic coherence shows new features. There is a non-vanishing probability for the atom emitting a photon in the cavity even when the resonance condition is not fulfilled (here the resonance condition means that the cavity length is an integer multiple of half the atomic de Broglie wavelength). Under the resonance condition, the atomic emission probability has two sets of resonance peaks. For a very strong coherent driving field, the emission of the atom can be forbidden. As to the photon statistics, when the driving field is not very strong, the driving-induced atomic coherence reduces the photon number fluctuations of the cavity field. The photon statistics exhibits strong sub-Poissonian behaviour. In the region considered here, it can even be sub-Poissonian for any cavity length. However, when the driving field is too strong, the sub-Poissonian property may disappear.
We derive an expression of the interaction between a quantum cavity field and an ultracold A-type three-level atom in which two upper levels are coupled by a coherent driving field. The effects of the driving-induced atomic coherence on the atomic emission probability are investigated. It is found that, due to the driving-induced atomic coherence, there are two transition channels for the atom interacting with the cavity field. Between the two transition channels, there is a quantum interference, which is a destructive interference. This destructive quantum interference suppresses the emission of the atom. The atomic emission probability decreases with the increasing driving field.
The idea of the two-photon mazer (microwave amplification via z -motion-induced emission of radiation) is put forward. The dressed states for the interaction of a cascade three-level atom with a quantum cavity field are derived. The general quantum theory of the two-photon mazer is established and its emission probability is studied. The effects of the atomic c.m. momentum and of the atom-field detuning are examined. It is found that the two-photon mazer shows new features that differ from both the one-photon mazer and the conventional two-photon micromaser.
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 derive an expression of the interaction between a quantum cavity field and an ultracold Λ-type three-level atom in which two upper levels are coupled by a coherent driving field. The effects of the driving-induced atomic coherence on the atomic emission probability are investigated. It is found that, due to the driving-induced atomic coherence, there are two transition channels for the atom interacting with the cavity field. Between the two transition channels, there is a quantum interference, which is a destructive interference. This destructive quantum interference suppresses the emission of the atom. The atomic emission probability decreases with the increasing driving field.
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.
The properties of the two-mode mazer operating on V-type three-level atoms are studied. The effect of the one-atom pumping on the two modes of the cavity field in number-state is asymmetric, that is, the atom emits a photon into one mode with some probability and absorbs a photon from the other mode with some other probability. This effect makes the steady-state photon distribution and the steady-state photon statistics asymmetric for the two modes. The diagram of the probability currents for the photon distribution, given by the analysis of the master equation, reveals that there is no detailed balance solution for the master equation. The computations show that the photon statistics of one mode or both modes can be sub-Poissonian, that the two modes can have anticorrelation or correlation, that the photon statistics increases with the increase of thermal photons and that the resonant position and strength of the photon statistics are influenced by the ratio of the two coupling strengths of the two modes. These properties are also discussed physically.