Dynamic photon heat transport through a mesoscopic Josephson device biased by dc and ac voltages

Photon heat transport through a mesoscopic Josephson junction (MJJ) device under the perturbation of dc and ac voltages has been investigated, where the MJJ device is coupled to photon reservoirs, and the Caldeira-Leggett circuit theory has been used. The photon heat current and differential heat conductance have been evaluated to show the dynamic behaviors governed by the applied fields. The dc voltage V induces time t oscillating supercurrent with frequency ω=2eV∕ħ. The ac voltage Ṽcos(Ω0t) generates a series of supercurrent branches relating to the ac voltage frequency Ω0 and its magnitude Ṽ. The photon heat current is determined by the superposition of different heat current branches induced by the dc and ac fields. The frequencies ω and Ω0 relating to dc and ac fields play important role in controlling the photon heat current and conductance. The detailed magnitude and oscillation structure are strongly dependent on the frequency ratio ω∕Ω0, and the scaled magnitude of ac field Λ=2eṼħΩ0. Resonant heat current appears when ω and Ω0 possess commensurate relations, where the superposition of heat current branches displays coherent interference. As ω and Ω0 possess incommensurate relations, heat current is much smaller, and it fluctuates fiercely compared with the commensurate cases. Beat-like resonance emerges by tuning the frequencies ω and Ω0 at some definite values of Coulomb energy.