  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.
