Quantum thermal transport and two-photon statistics serve as two representative nonequilibrium features in circuit quantum electrodynamics systems. Here, we investigate quantum heat flow and two-photon correlation function at steady-state in a composite qubit-resonator model, where one qubit shows both transverse and longitudinal couplings to a single-mode optical resonator. With weak qubit-resonator interaction, we unravel two microscopic transport pictures, i.e., cotunneling and cyclic heat exchange processes, corresponding to transverse and longitudinal couplings respectively. At strong qubit-resonator coupling, the heat current exhibits nonmonotonic behavior by increasing qubit-resonator coupling strength, which tightly relies on the scattering processes between the qubit and corresponding thermal bath. Furthermore, the longitudinal coupling is preferred to enhance heat current in strong qubit-resonator coupling regime. For two-photon correlation function, it exhibits an antibunching-to-bunching transition, which is mainly dominated by the modulation of energy gap between the first and second excited eigenstates. Our results are expected to deepen the understanding of nonequilibrium thermal transport and nonclassical photon radiation based on the circuit quantum electrodynamics platform.
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