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Quantum thermal transport and two-photon statistics serve as tworepresentative nonequilibrium features in circuit quantum electrodynamicssystems. Here, we investigate quantum heat flow and two-photon correlationfunction at steady-state in a composite qubit-resonator model, where one qubitshows both transverse and longitudinal couplings to a single-mode opticalresonator. With weak qubit-resonator interaction, we unravel two microscopictransport pictures, i.e., cotunneling and cyclic heat exchange processes,corresponding to transverse and longitudinal couplings respectively. At strongqubit-resonator coupling, the heat current exhibits nonmonotonic behavior byincreasing qubit-resonator coupling strength, which tightly relies on thescattering processes between the qubit and corresponding thermal bath.Furthermore, the longitudinal coupling is preferred to enhance heat current instrong qubit-resonator coupling regime. For two-photon correlation function, itexhibits an antibunching-to-bunching transition, which is mainly dominated bythe modulation of energy gap between the first and second excited eigenstates.Our results are expected to deepen the understanding of nonequilibrium thermaltransport and nonclassical photon radiation based on the circuit quantumelectrodynamics platform.

Tuning nonequilibrium heat current and two-photon statistics via composite qubit-resonator interaction