We develop a generic model for a cyclic quantum heat engine that makes it possible to coherently amplify a periodically modulated input signal without the need to couple the working medium to multiple reservoirs at the same time. Instead, we suggest an operation principle that is based on the spontaneous creation of population inversion in incomplete relaxation processes induced by periodic temperature variations. Focusing on Lindblad dynamics and systems with equally spaced energy levels, e.g. qubits or quantum harmonic oscillators, we derive a general working criterion for such cyclic quantum amplifiers. This criterion defines a class of candidates for suitable working media and applies to arbitrary control protocols. For the minimal case of a cyclic three-level amplifier, we show that our criterion is tight and explore the conditions for optimal performance.

8 pages, 4 figures