Photonic heat transport from weak to strong coupling

Superconducting circuits provide a favorable platform for quantum thermodynamic experiments. An important component for such experiments is a heat valve, i.e. a device which allows one to control the heat power flowing through the system. Here we theoretically study the heat valve based on a superconducting quantum interference device (SQUID) coupled to two heat baths via two resonators. The heat current in such system can be tuned by magnetic flux. We investigate how does the heat current modulation depend on the coupling strength g between the SQUID and the resonators. In the weak coupling regime the heat current modulation grows as g2, but, surprisingly, at the intermediate coupling it can be strongly suppressed. This effect is linked to the resonant nature of the heat transport at weak coupling, where the heat current dependence on the magnetic flux is a periodic set of narrow peaks. At the intermediate coupling, the peaks become broader and overlap, thus reducing the heat modulation. At very strong coupling the heat modulation grows again and finally saturates at a constant value.