Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Xing, Wanli, Ralph, Timothy C.
Institutions: UNSW Sydney, The University of Queensland
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224899406