The qutrit as a heat diode and circulator

We investigate the heat transport properties of a three-level system coupled to three thermal baths, assuming a model based on superconducting circuit implementations. The system-bath coupling is mediated by resonators which serve as frequency filters for the different qutrit transitions. Taking into account the finite quality factors of the resonators, we find thermal rectification and circulation effects not expected in configurations with perfectly-filtered couplings. Heat leakage in off-resonant transitions can be exploited to make the system work as an ideal diode where heat flows in the same direction between two baths irrespective of the sign of the temperature difference, as well as a perfect heat circulator whose state is phase-reversible.