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.
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 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 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.