Revealing beyond-mean-field correlations in a nuclear ensemble via a proxy qubit

A coherent ensemble of spins interfaced with a proxy qubit is an attractive platform to create many-body coherences and probe the regime of collective excitations. An electron spin qubit in a semiconductor quantum dot is a realisation of such an interface to a dense nuclear spin ensemble consisting of multiple high-spin species. To date, this electron has relayed properties of its nuclear environment via the statistics of its mean-field interaction with the total nuclear polarisation, namely its mean and variance. Here, we demonstrate a species-selective spin-state reconstruction of a nuclear ensemble that instead exploits its response to the electron-mediated injection of collective nuclear excitations. For the accessible range of optically prepared mean fields, the reconstructed populations evidence a non-thermal, correlated nuclear state. The sum over reconstructed species-resolved polarisations exceeds threefold our prepared mean field. This stark deviation follows from a spin ensemble that contains coherences, and manifests the formation of a dark many-body state.