  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.
