  We propose a quantum thermal machine composed of two nanomechanical
resonators (NMR) (two membranes suspended over a trench in a substrate), placed
a few $\mu$m from each other. The quantum thermodynamical cycle is powered by
the Casimir interaction between the resonators and the working fluid is the
polariton resulting from the mixture of the flexural (out-of-plane) vibrations.
With the help of piezoelectric cells, we select and sweep the polariton
frequency cyclically. We calculate the performance of the proposed quantum
thermal machines and show that high efficiencies are achieved thanks to (i) the
strong coupling between the resonators and (ii) the large difference between
the membrane stiffnesses. Our findings can be of particular importance for
applications in nanomechanical technologies where a sensitive control of
temperature is needed.

Quantum Physics;Other Condensed Matter;Quantum Gases