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.

💡 Research Summary

The manuscript addresses a central challenge in continuous‑variable quantum optics: how to certify the nonclassical character of non‑Gaussian states that remain “coherent to all orders.” Generalized coherent states (GCS) arise when an ordinary coherent state propagates through a nonlinear medium described by a Hamiltonian proportional to a power of the photon‑number operator, (\hat H_{\rm int}\propto\hat n^{\varepsilon}). Although GCS retain the Poissonian photon‑number distribution of a coherent state, they can exhibit Wigner‑function negativity, enhanced quantum Fisher information, and other resources valuable for quantum information processing and precision metrology. Traditional intensity‑intensity correlations, such as the second‑order Glauber function (g^{(2)}), fail to reveal any quantum signature because the relevant normally‑ordered moments (\langle:\hat a^{\dagger m}\hat a^{m}:\rangle) are identical to those of a coherent state.

The authors propose to use a lower‑order mixed correlation, the intensity‑field correlation function \