Characterization of Generalized Coherent States through Intensity-Field Correlations

Non-Gaussian quantum states of light are essential resources for quantum information processing and precision metrology. Among them, generalized coherent states (GCS), which naturally arise from the evolution of a coherent state with a nonlinear medium, exhibit useful quantum features such as Wigner negativity and metrological advantages [Phys. Rev. Res. 5, 013165 (2023)]. Because these states remain coherent to all orders, their nonclassical character cannot be revealed through standard intensity-intensity correlation measurements. Here, we demonstrate that the intensity-field correlation function alone provides a simple and experimentally accessible witness of nonclassicality. For GCSs, any deviation of this normalized correlation from unity signals nonclassical behavior. We derive analytical results for Kerr-generated states and extend the analysis to statistical mixtures of GCSs. The proposed approach enables real-time, low-complexity detection of quantum signatures in non-Gaussian states, offering a practical tool for experiments across a broad range of nonlinear regimes.