The formation of entangled Schr\"odinger cat-like states in the process of spontaneous parametric down-conversion

TL;DR

This paper explores the generation of entangled Schrödinger cat-like states via fully quantum modeling of spontaneous parametric down-conversion, revealing non-Gaussian features, squeezing, and high-dimensional entanglement.

Contribution

It provides a fully quantum analysis of SPDC with a depleted pump, demonstrating non-Gaussian entangled states and higher-dimensional entanglement structures.

Findings

Significant squeezing up to 4.04 dB in degenerate SPDC.

Non-Gaussian states with interference patterns observed.

Higher Schmidt number (~10.38) in non-degenerate SPDC indicating complex entanglement.

Abstract

We investigate entangled Schr\"odinger cat-like states (SCLSs) in degenerate and non-degenerate spontaneous parametric down-conversion (SPDC) with a fully quantized, depleted pump. Our fully quantum treatment, visualized via Wigner functions, reveals non-Gaussian features and interference patterns absent in semiclassical models. For degenerate SPDC, we demonstrate significant squeezing (up to $4.04\,\mathrm{dB}$) and robust super-Poissonian statistics in both non-dissipative and dissipative regimes. Extending to non-degenerate SPDC, we confirm that pump quantization also generates non-Gaussian states in all modes and yields a higher-dimensional entanglement structure, evidenced by a larger Schmidt number ($K^{(\mathrm{ND})} \approx 10.38$) compared to the degenerate case ($K \approx 1.93$). Our approach captures critical dynamics like energy exchange and phase-dependent evolution. These entangled SCLSs, non-Gaussian states realizable in $\chi^{(2)}$ media at moderate intensities and offering advantages over $\chi^{(3)}$-based schemes, are promising resources for quantum sensing and information processing.