Quantum noise dynamics in nonlinear pulse propagation

TL;DR

This paper introduces a Gaussian-state model and a Gaussian split-step Fourier method to simulate quantum noise and entanglement in nonlinear ultrafast pulse propagation, enabling efficient analysis of complex multimode quantum dynamics.

Contribution

It develops a nonlinear, Gaussian-state based numerical approach for modeling quantum fluctuations in broadband ultrafast nonlinear optics systems.

Findings

Efficient GSSF method evaluates in $O(M^2 ext{log} M)$ time.

Model captures nonlinear quantum dynamics including entanglement.

Demonstrates applicability to various ultrafast nonlinear optical systems.

Abstract

The propagation of ultrafast pulses in dispersion-engineered waveguides, exhibiting strong field confinement in both space and time, is a promising avenue towards single-photon nonlinearities in an all-optical platform. However, quantum engineering in such systems requires new numerical tools and physical insights to harness their complicated multimode and nonlinear quantum dynamics. In this work, we use a self-consistent, multimode Gaussian-state model to capture the nonlinear dynamics of broadband quantum fluctuations and correlations, including entanglement. Notably, despite its parametrization by Gaussian states, our model exhibits nonlinear dynamics in both the mean field and the quantum correlations, giving it a marked advantage over conventional linearized treatments of quantum noise, especially for systems exhibiting gain saturation and strong nonlinearities. Numerically, our approach takes the form of a Gaussian split-step Fourier (GSSF) method, naturally generalizing highly efficient SSF methods used in classical ultrafast nonlinear optics; the equations for GSSF evaluate in $O(M^2\log M)$ time for an $M$-mode system with $O(M^2)$ quantum correlations. To demonstrate the broad applicability of GSSF, we numerically study quantum noise dynamics and multimode entanglement in several ultrafast systems, from canonical soliton propagation in third-order ($\chi^{(3)}$) waveguides to saturated $\chi^{(2)}$ broadband parametric generation and supercontinuum generation, e.g., as recently demonstrated in thin-film lithium niobate nanophotonics.