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Physical Review A

Quantum theory of the two-photon mazer: Emission probability

Zhi‐Ming Zhang, Zhiyuan Lu, Lin-sheng He

Published Jan 1, 1999• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.59.808

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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.
The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.
The analytical form of the emission probability produced by the interaction of an ultracold three-level atom with an electromagnetic bimodal cavity field with multi-photon transitions of the atoms (multi-photon mazer) is analysed in the framework of the dressed-state formalism, but is distinguished from other treatments by the inclusion of the spatial variation along the cavity axis. In particular, the cavity field mode profile is considered by using the mesa-mode function and differences in the collapse–revival patterns are reported. We demonstrate that, when propagation effects are taken into consideration, the emission probability is influenced significantly. We provide the necessary arguments to justify the validity of our conclusions for emission probability and the micromaser, whose dynamics are governed by the wavefunction. Our main conclusion is that, in the present system, the inclusion of the spatial dependence is necessary and important. The numerical illustrations provide evidence that, in cases of physical interest, the emission probability can be significant and can be reliably estimated for a broad range of field parameters using the present formalism.
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 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.
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.
Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.