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We propose a quantum heat engine composed of two superconducting transmissionline resonators interacting with each other via an optomechanical-likecoupling. One resonator is periodically excited by a thermal pump. Theincoherently driven resonator induces coherent oscillations in the other onedue to the coupling. A limit cycle, indicating finite power output, emerges inthe thermodynamical phase space. The system implements an all-electrical analogof a photonic piston. Instead of mechanical motion, the power output isobtained as a coherent electrical charging in our case. We explore thedifferences between the quantum and classical descriptions of our system bysolving the quantum master equation and classical Langevin equations.Specifically, we calculate the mean number of excitations, second-ordercoherence, as well as the entropy, temperature, power and mean energy to revealthe signatures of quantum behavior in the statistical and thermodynamicproperties of the system. We find evidence of a quantum enhancement in thepower output of the engine at low temperatures.

A quantum heat engine with coupled superconducting resonators