The concept of a quantum heat pump is proposed as a convenient model in the thermodynamic interpretation of certain multilevel processes. The ideal quantum heat engine is defined as an idealization of realistic pumped multilevel systems in much the same way that the well-known Carnot cycle is an idealization of physically realizable, classical processes or engines. There is evidence that the conventional Carnot cycle can be operated only between reservoirs at absolute temperatures of identical sign. No such restriction applies, however, to the quantum heat engine. Thus it may be used to calibrate negative absolute temperatures by relating them directly to positive temperatures. Negative efficiencies or efficiencies greater than unity have particularly simple interpretations in the quantum-heat-engine model. An important application of these concepts is in the calculation of optical maser parameters.

• Received 27 October 1966

DOI:https://doi.org/10.1103/PhysRev.156.343