  We calculate the normalized second-order correlation function for a system of
two tunnel-coupled photonic resonators, each one exhibiting a single-photon
nonlinearity of the Kerr type. We employ a full quantum formulation: the master
equation for the model, which takes into account both a coherent continuous
drive and radiative as well as non-radiative dissipation channels, is solved
analytically in steady state through a perturbative approach, and the results
are compared to exact numerical simulations. The degree of second-order
coherence displays values between 0 and 1, and divides the diagram identified
by the two energy scales of the system - the tunneling and the nonlinear Kerr
interaction - into two distinct regions separated by a crossover. When the
tunneling term dominates over the nonlinear one, the system state is
delocalized over both cavities and the emitted light is coherent. In the
opposite limit, photon blockade sets in and the system shows an insulator-like
state with photons locked on each cavity, identified by antibunching of emitted
light.
