$N$ scaling of large-sample collective decay in inhomogeneous ensembles

We experimentally study collective decay of an extended disordered ensemble of $N$ atoms inside a hollow-core fiber. We observe up to 300-fold enhanced decay rates, strong optical bursts, and a coherent ringing. Due to inhomogeneities limiting the synchronization of atoms, the data does not show the typical scaling with $N$. We show that an effective number of collective emitters can be determined to recover the $N$ scaling known to homogeneous ensembles over a large parameter range. This provides physical insight into the limits of collective decay and allows for its optimization in extended ensembles as used, e.g., in quantum optics, precision time-keeping, or waveguide QED.