Analytic Solutions To Fully Quantized Parametric Amplification
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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BibTeX
@misc{xing2026analytic,
title = {{Analytic Solutions To Fully Quantized Parametric Amplification}},
author = {Wanli Xing and Timothy C. Ralph},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39387},
eprint = {2610.39387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39387},
}
RIS
TY - UNPB
TI - Analytic Solutions To Fully Quantized Parametric Amplification
AU - Wanli Xing
AU - Timothy C. Ralph
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39387
UR - https://arxiv.org/abs/2610.39387
AB - 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.
ER -