We study the heat transfer between $N$ coupled quantum resonators with applied synthetic electric and magnetic fields realized by changing the resonator parameters by external drivings. To this end we develop two general methods, based on the quantum optical master equation and on the Langevin equation for $N$ coupled oscillators where all quantum oscillators can have their own heat baths. The synthetic electric and magnetic fields are generated by a dynamical modulation of the oscillator resonance with a given phase. Using Floquet theory, we solve the dynamical equations with both methods, which allow us to determine the heat flux spectra and the transferred power. We apply these methods to study the specific case of a linear tight-binding chain of four quantum coupled resonators. We find that, in that case, in addition to a nonreciprocal heat flux spectrum already predicted in previous investigations, the synthetic fields induce here nonreciprocity in the total heat flux, hence realizing a net heat flux rectification.

• Received 12 June 2023
• Accepted 18 September 2023

DOI:https://doi.org/10.1103/PhysRevA.108.042201