Optimizing Wigner Negativity in Scattering Processes Using Energetic Cost Functions

Abstract:Wigner negativity is a key resource for quantum technologies but is difficult to optimize in multimode scattering systems. We study the scattering of coherent pulses by a two-level emitter coupled to a one-dimensional waveguide and introduce energetic cost functions that enable the optimization of Wigner negativity without reconstructing the full Wigner function. By decomposing the scattered energy into coherent, thermal, squeezing, and non-Gaussian contributions, we identify an energetic witness that strongly correlates with the achievable negativity across all driving regimes. This approach singles out optimal output temporal modes and uncovers operating points generating appreciable Wigner negativity with sub-photon input energies. We further identify a maximal energy-efficiency regime at spectral mode matching, where the emitter effectively implements a vacuum-selective $\pi$ phase shift, realizing a giant optical nonlinearity. These results establish energetic optimization as a practical route to engineering Wigner-negative photonic states in waveguide quantum electrodynamics and related bosonic scattering platforms.

5 Pages Main Text, 2 Page End Matter, 6 Pages Supplemental. 9 Figures (7 Main, 5 Supplementary). Comments are welcomed!

arXiv:2606.15101 [quant-ph]

(or arXiv:2606.15101v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.15101 Focus to learn more arXiv-issued DOI via DataCite

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