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Japanese Journal of Applied Physics

Theoretical Considerations of the Three-Level Maser Detector for the Far-Infrared

Kōichi Shimoda

Published May 1, 1967• 7 citations
Publisher

Abstract

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.

DOI
10.1143/jjap.6.620

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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 quantum mechanical behavior of the three-level maser was experimentally studied using the rotational spectrum of HCOOH molecule at microwave frequencies. By using the 2 11 ←1 10 line at the frequency of 46581 Mc as the pumping, the induced emission of the 2 11 →2 12 line at the frequency of 4916 Mc was obtained. For a strong pumping, the splitting of emission line due to resonant modulation effect was observed. The line-shape of emission signal under off-resonant pumping was studied in detail. The emission spectrum due to simultaneous emission and absorption of two photons corresponding to the signal and the pumping was observed for the condition of far off-resonant pumping. The results were compared with the theory described in the previous paper, and was found to be in good agreement in many respects. Some discrepancies concerning emission intensity are also discussed. An application of the multiple quantum transition to a four-level system of HC·OOH is described.
We present a theoretical model of an on-chip three-level maser in a superconducting circuit based on a single artificial atom and pumped by a temperature gradient between thermal baths coupled to different interlevel transitions. We show that maser powers of the order of a few femtowatts, well exceeding the resolution of the sensitive bolometry, can be achieved with typical circuit parameters. We also demonstrate that population inversion in the artificial atom can be detected without measuring coherent radiation output of the maser. For that purpose, the system should operate as a three-terminal heat transport device. The hallmark of population inversion is the influx of heat power into the weakly coupled output terminal even though its temperature exceeds the temperatures of the two other terminals. The proposed method of on-chip conversion of heat into microwave radiation and control of energy-level populations by heating provide additional useful tools for circuit quantum electrodynamics experiments.
Small differences between the emission and absorption spectra of three-level maser centers can have a pronounced effect on maser operation. This paper considers the effects of a Stokes shift, the simplest and most probable difference. If there is a Stokes shift which is large compared to the linewidth, the operation of the maser will be essentially four level. If there is a small Stokes shift (some fraction of the linewidth) the operation will still be three level, but the Stokes shift will significantly affect the operation of the maser. The principal effects will be a shift of the maser line from the peak in the fluorescent emission line (away from the absorption peak) and a reduction in the upper level population required to reach the threshold of oscillation. The evidence is not conclusive as to whether there is a Stokes shift in the ruby R1 line, but if there is a shift it is at most a small fraction of the fluorescent linewidth at room temperature. Shifts of the ruby maser line to the red have been observed by D'Haenens and Asawa and have been attributed to large temperature changes. It is likely that the temperature shift, while important, will not explain the shift which has been observed. Gires and Mayer have found the lower state population of an operating ruby maser to be approximately 75% of the unexcited population rather than approximately 50% and have suggested a Stokes shift as a possible cause of the reduction in the upper state population at threshold. This paper considers the effect of such a small Stokes shift on the operation of an otherwise ideal three-level maser.
A three-level system which radiates at both intermediate transition frequencies is considered to be coherently pumped at a frequency near the two-photon resonance frequency. A sharply resonant rise in the second- and third-level population is found for slight detuning of the pump from two-photon resonance. Population inversion in either transition is shown to be possible, depending on the pertinent parameters. This effect furnishes a novel method of population inversion at a frequency higher than the pump frequency. Keywords include: Laser, Laser-type devices, Coherent pumping, Three-level systems, and Quantum electronics.
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.