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arXiv · 2405.14526

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

Ranjit Singh·Alexander E. Teretenkov
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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.

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Ranjit Singh, Alexander E. Teretenkov. 2024-05-23. The formation of entangled Schr\"odinger cat-like states in the process of spontaneous parametric down-conversion. https://doi.org/10.1016/j.physleta.2026.131382

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