Multiensemble Superradiance for Distributed Quantum Sensing

Multiensemble superradiance extends Dicke superradiance to multiple ensembles and supports dark states whose properties depend on the initial state. In the large-$N$ limit, we derive analytical covariance matrices for these dark states, revealing inter-ensemble entanglement that enhances quantum metrology. The minimum eigenvalue, determined by the curvature of the superradiance potential, corresponds to the optimal multiparameter spin-squeezing coefficient, which is given by the \emph{Rayleigh quotient} of the spin-squeezing matrix, linking metrological sensitivity to the geometric structure of the underlying dynamics. The multiparameter squeezing coefficient provides a variational framework for optimizing metrological performance. These results enable optimal estimation of arbitrary linear combinations of multiple parameters, offering a concrete protocol for distributed quantum sensing and a promising route toward multimode quantum interferometry.