Superlinear scaling of cavity cooperativity via selective radiance in atomic arrays

We demonstrate that the collective coupling of an atom array to a cavity can be increased beyond the conventional linear scaling with atom number. Exploiting selective radiance, one can harness the collimated emission of the array to enhance its coupling to the cavity mode, while simultaneously suppressing its coupling to other optical modes (i.e., the modes for transverse spontaneous emission out of the cavity). We develop a spin model describing field-mediated atomic interactions via a Green’s function for the combined “free space + cavity” environment that cleanly separates cavity channels from the radiative continuum, excludes far-field directions blocked by the mirrors, and avoids double-counting optical modes. Using this formalism, we predict an effective cavity cooperativity that scales superlinearly with atom number. We expect such behavior to be observable in state-of-the-art experimental platforms with arrays of N~30 atoms.