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arXiv · 2610.39387

Analytic Solutions To Fully Quantized Parametric Amplification

Wanli Xing·Timothy C. Ralph
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Abstract

We derive analytic expressions for observable dynamics under the fully quantized trilinear Hamiltonian, governing quantum three-wave mixing and parametric amplification. Starting from a coherent pump and vacuum signal and idler, the calculation reorganizes the Heisenberg expansion into resummed depletion and return profiles, yielding directly evaluable expressions for all 1st-, 2nd- and 3rd-order correlations. The construction uses no parametric approximation or fitted parameters. Representative numerical benchmarks show errors of order $10^{-12}$ throughout the entire pump depletion, and below $10^{-3}$ across dozens of depletion-and-back-conversion cycles, up to the first total collapse of the oscillation. The first-depletion treatment additionally provides 4th-order correlations, accommodates bright squeezed-pump inputs and reveals phenomena important to future optical quantum technologies. The framework can be extended to higher moments.

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Wanli Xing, Timothy C. Ralph. 2026-10-29. Analytic Solutions To Fully Quantized Parametric Amplification. https://arxiv.org/abs/2610.39387

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