Mesoscopic photon heat transistor

We show that the heat transport between two bodies, mediated by electromagnetic fluctuations, can be controlled with an intermediate quantum circuit--leading to the device concept of a mesoscopic photon heat transistor (MPHT). Our theoretical analysis is based on a novel Meir-Wingreen-Landauer-type of conductance formula, which gives the photonic heat current through an arbitrary circuit element coupled to two dissipative reservoirs at finite temperatures. As an illustration we present an exact solution for the case when the intermediate circuit can be described as an electromagnetic resonator. We discuss in detail how the MPHT can be implemented experimentally in terms of a flux-controlled SQUID circuit.