Hybrid Measurement of Atomic Ensembles for Generating Nonclassical States

We present a protocol for generating nonclassical states of atomic spin ensembles through the backaction induced by a hybrid measurement, which combines homodyne and single photon detection. By squeezing the atomic ensemble via homodyne detection followed by coherent control, one can effectively increase the coupling strength between the ensemble and a probe beam. This enhancement could prove useful in the absence of an atomic cavity. We benchmark the protocol's utility using Wigner function negativity and Fisher information as measures of quantum advantage, and we study the decay of these quantities under the effects of decoherence. We employ the Holstein-Primakoff approximation to study the atomic ensemble using a bosonic mode, and analytically study the evolution of the state under the combined effects of simultaneous measurement and optical pumping.