Characterization of Generalized Coherent States through Intensity-Field Correlations

TL;DR

The paper develops a practical, low-order nonclassicality witness for generalized coherent states, showing that the intensity-field correlation $g^{(3/2)}_{\theta}$ deviates from unity whenever a GCS exhibits nonclassical features, despite GCSs being coherent to all orders. It provides analytical results for Kerr states ($\varepsilon=2$), revealing simple closed-form expressions and revival to coherence at specific times, while also covering general $\varepsilon$ and mixtures. The authors further analyze robustness to intense-light regimes and photon loss, highlighting the connected correlator $G^{(3/2)}_{c,\theta}$ as a reliable indicator of nonclassicality even when Wigner negativity diminishes. Overall, the work offers a practically accessible, real-time diagnostic tool for detecting non-Gaussian quantum signatures across a broad nonlinear landscape.

Abstract

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.

Figures (4)

• Figure 1: Optical setup to measure the intensity-field correlation function. A GCS state $\ket{\alpha_{\varepsilon,t}}$ is split on a beam-splitter. Part of the state is sent to an intensity detector and the other part is mixed with a local oscillator (LO$_\theta$) to measure the quadrature along $\theta$.
• Figure 2: Normalized intensity-field correlation function (a) and Wigner negativity (b) as a function of the rescaled time $t_\varepsilon=2t/\varepsilon$ for $\varepsilon=0.5$ (solid green), $\varepsilon=2$ (dashed blue) and $\varepsilon=3$ (dashed-dotted orange). The dashed gray line corresponds to the classical limit. The insets show the time evolution of $g^{(3/2)}_{\theta}$ for different local oscillator phases $\theta =\arg\langle\hat{a}\rangle+\delta\phi$, near the time point where $g^{(3/2)}_{\theta=\arg\langle \hat{a} \rangle}$ crosses the classical limit 1. The color intensity encodes the supplemental phase $\delta\phi=-\pi/3,-\pi/6,0, \pi/6,\pi/3$ from lighter to darker, respectively. Here the mean particle number is $\langle\hat{n}\rangle=1$.
• Figure 3: Evolution of $|G^{(3/2)}_{c,\,\theta}|/|\alpha|^{3/2}$ as a function of time $t$ and the initial displacement $|\alpha|$ for $\varepsilon=0.5$ (a), $2$ (b) and $3$ (c). A positive value witnesses nonclassicality of the CGS and the intensity of the color encode the value of $|G^{(3/2)}_{c,\,\theta}|/|\alpha|^{3/2}$. The colors of the heatmaps match the ones of Fig. \ref{['fig1']}.
• Figure 4: Connected intensity-field correlation function (a) and Wigner negativity (b) as a function of losses $1-\eta$ for different Kerr state parametrized by $t=0.15,\, \pi/4,$ and $\pi/2$, respectively plotted with solid, dashed and dotted lines. The inset shows the normalized intensity field correlation function, which is constant up to $\eta=0$, for which the value is 1.