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Physical Review

Role of Double-Quantum Transitions in Masers

Shaul Yatsiv

Published Mar 15, 1959• 27 citations
Publisher

Abstract

A generalized treatment of a three-level maser as an example of double-irradiation experiments is based on a previous analysis of multiple-quantum transitions in nuclear magnetic resonance. The emphasis in the present treatment, as distinct from other expositions of the same problem, is on the role of the double-quantum transitions. In particular, conditions are found in which the maser operation is mainly governed by the double-quantum process and does not require a true "pumping" stage. Such a case is realizable in practice but its technical applicability is questionable. A study of the behavior of various transitions in this example is instructive for understanding the general role of the double-quantum transitions in double-resonance experiments.

DOI
10.1103/physrev.113.1538

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The Journal of Chemical Physics•Dec 15, 1970•49 citations
A generalized treatment of a three-level maser as an example of double-irradiation experiments is based on a previous analysis of multiple-quantum transitions in nuclear magnetic resonance. The emphasis in the present treatment, as distinct from other expositions of the same problem, is on the role of the double-quantum transitions. In particular, conditions are found in which the maser operation is mainly governed by the double-quantum process and does not require a true "pumping" stage. Such a case is realizable in practice but its technical applicability is questionable. A study of the behavior of various transitions in this example is instructive for understanding the general role of the double-quantum transitions in double-resonance experiments.
The multiple quantum process in the off-resonant condition of the three-level gas maser is discussed. The intensity of the emission produced by this process is calculated by a perturbation theory and also by a more general treatment which is the application of Javan's theory to the off-resonant case. Some graphical representations of the signal line under off-resonant pumping are given for the purpose of comparison with experiment. The Doppler effect in three-level maser action is analyzed from both semiclassical and quantum mechanical points of view under the presence of collision relaxation. It was shown that in a saturation process between two levels, Doppler effect behaves as to contribute to both line-width and relaxation time for the transition, and that under strong pumping, Doppler effect in pumping transition has a marked influence on both intensity and shape of the signal line through the effect of multiple quantum transition.
In the case when the pumping transition in a three-level system of a molecule does not exactly coincide with the output frequency of a maser oscillator, four different types of operation at off-resonance of the three-level maser detector are discussed. At first the use of pressure broadening is considered; secondly a method which observes the double-quantum transition and thirdly the other method which measures a change in population caused by the double-quantum pumping are considered, and finally the level shift due to the far-infrared input is considered. It is found that the third method of double-quantum pumping in which three waves are involved is the most sensitive. The minimum detectable power of order 10-6W/cm2 with the resolving time of about 10-6s is expected in detecting the maser output at the far-infrared which differs from the resonant frequency of the detector by as large as 10 GHz.
In a three-level maser, a transition between two energy levels is saturated in order to produce an induced emission of power at a lower frequency corresponding to a transition between an intermediate energy level and one or the other of the two saturated levels. In this paper, certain effects are discussed which cannot be predicted from a theory in which the population differences alone are considered in this process. For instance, it is shown that, in some cases it is possible to obtain for the same system an induced emission of power at two frequencies given by the resonances between the intermediate energy level and both of the saturated levels. Also, it is shown that, even in the absence of inhomogeneous broadening of the spectral line, one can obtain a net induced emission at some portions of a resonant line and a net absorption at other frequencies within the line widths. Such effects become important even in early stages of saturation in cases where T1=T2{T}_{1}={T}_{2}T1​=T2​ which is true for ordinary gaseous systems and individual spin systems in a majority of very dilute paramagnetic solids. A complete theory is discussed for a gaseous system and extended to two limiting cases of paramagnetic materials with T1=T2{T}_{1}={T}_{2}T1​=T2​ and ${T}_{2}\ensuremath{\ll}{T}_{1}$ for each individual spin system. Furthermore, it is shown that for a saturating field of fixed frequency, the integral of induced power over the entire line is in full agreement with the results of a semiclassical treatment in which the population differences alone are considered. Some remarks are made as to the practicability of certain systems of this type.
The expression for the absorption coefficient in two-photon resonance transitions is deduced under general conditions. No particular restrictions are imposed on the level system or on the frequencies and intensities of the fields. The following cases are considered: (i) a two-level system (with and without singularities) irradiated by a single wave and (ii) a three-level system irradiated by two waves. Some theoretical and experimental disagreements reported by authors of previous papers are examined and clarified by the present theory.
Since the demonstration of the possibility of achieving very low noise amplification of signals in the centimetric wavebands, a great deal of work has been carried out in various laboratories with a view to producing and testing devices. The major part of the present article focuses attention on one particular device, the three-level solid-state maser. The physical principles underlying the process of stimulated emission of radiation are in many cases unfamiliar to electronic engineers, and study of the growing literature on the subject can be confusing without a clear understanding of the physics involved. The present article outlines the general theory of emission and radiation processes, particularly as they apply to the microwave spectrum. A quantum mechanical description is employed throughout, and a brief and not very rigorous account is given of the relevant portions of this theory as it applies to the investigation of transistors between energy levels. Well-known expressions are derived for the operating characteristics of a three-level maser, particular attention being given to the significance of the various factors involved and their relationship to easily measured quantities. Little information is included concerning practical maser amplifiers; at the time of writing, few practical devices had been constructed. A survey of recent literature indicates the rapid progress which has since been made, and shows the interest in the development of masers.
A general theory has been developed to calculate the response, in NMR conditions, of a spin system irradiated by two nearly resonant waves having different frequencies and intense enough to produce an appreciable saturation. The absorption signal has been calculated employing the statistical operator technique, treating the electromagnetic field by the second quantization formalism. Two kinds of transitions are expected: The first one arises from processes in which n photons of one wave are emitted and n photons of the other wave are absorbed, the second one arises from processes involving the emission of n photons of one wave and the absorption of n ± 1 photons of the other. In the first case all the transitions coalesce in a single dispersionlike signal, which occurs when the frequencies of the two waves are nearly the same; in the second case a many-line spectrum occurs in which emission and absorption lines are present. The experimental results here reported strictly agree with theoretical previsions.