Nonequilibrium energy transport and nonclassical correlations of photons in a two-mode circuit quantum electrodynamic system

We investigate nonequilibrium energy transport and nonclassical correlations of photons in a nonequilibrium two-mode circuit quantum electrodynamic system with noncommutative qubit-photon couplings. Our calculations include a quantum master equation, which can handle ultrastrong qubit-photon interactions. For weak qubit-photon couplings, the nonmonotonic behavior of nonequilibrium energy flow is explored for large temperature bias, stemming from the breakdown of microscopic energy transition cycles. Two distinct scaling features of the coupling parameters in energy currents are analytically shown. Moreover, the longitudinal qubit-photon coupling shows a dramatic contribution to the exhibition of antibunching behaviors of autocorrelation and violation of the Cauchy-Schwarz inequality of the cross correlation of photons. These results may provide insight into quantum energy modulation devices and photon correlation manipulation in circuit quantum electrodynamics.