Work and heat in conventional and measurement powered quantum heat engines*

We constructed a simple autonomous thermoelectric engine operated out of thermal equilibrium composed of two superconducting qubits coupled to separate heat baths and connected by a Josephson junction.
We showed that the fluctuations in the integrated work and heat over finite time intervals are not simply the variances of suitable system observables but employ more complex quantum correlation functions. In particular, the transfer of heat into the cold bath is equivalent to the process of spontaneous emission from a quantum light source and its temporal correlations follow from Glauber’s photodetection theory.
By investigating the conditional dynamics of the excitation propagating through the system by way of two-time correlation functions, we revealed the strokes of the engine underneath its constant steady state.
Finally, we went beyond the conventional engine design and considered a machine where the heat baths were replaced by a measurement protocol. We derived and analyzed its periodic steady state and showed that an adaptive measurement scheme allows a net positive work production on average–which offers an interesting basis for experimental implementation, especially when the size of the device does not permit an efficient separation between the heat baths.