How subradiance and superradiance affect the g⁽²⁾ correlations of photon emission in dense atom arrays

Superradiant and subradiant photon emission in dipole systems are typically associated with the g⁽²⁾ correlation showing bunched and antibunched behavior respectively. While the lifetime of the state determines the recovery time of the g⁽²⁾(τ) after emission, we are interested in studying how the instantaneous two-photon correlation, or the g⁽²⁾(τ = 0), is quantitatively dependent on the lifetimes of the single and double excitation eigenmodes of the system. We explore this in dense collectively interacting dipole systems like sub-wavelength arrays in the low-intensity regime. We also demonstrate a situation where we can control the g⁽²⁾(τ = 0) of a mode using the phase difference with another interfering mode of light. This can be used to suppress or promote two-photon emission in a particular mode. This effect is particularly pronounced when one mode is subradiant and the other is superradiant.