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arXiv:2307.05464

Quantum noise dynamics in nonlinear pulse propagation

Edwin Ng, Ryotatsu Yanagimoto, Marc Jankowski, M. M. Fejer, Hideo Mabuchi

Published Jul 11, 2023• 5 citations

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 ($χ^{(3)}$) waveguides to saturated $χ^{(2)}$ broadband parametric generation and supercontinuum generation, e.g., as recently demonstrated in thin-film lithium niobate nanophotonics.

DOI: 10.48550/arxiv.2307.05464

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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 (

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broadband parametric generation and supercontinuum generation, e.g., as recently demonstrated in thin-film lithium niobate nanophotonics.

Recent advances in nonlinear nanophotonics have enabled optical frequency conversion at energy scales remarkably close to the few-photon regime of quantum optics. A key technique in these efforts is dispersion engineering, allowing dynamical confinement of light into ultrashort pulses with high peak intensities. In this talk, we explore quantum effects expected to emerge in next-generation devices, with a focus on understanding how these phenomena interplay with the multimode physics of femtosecond pulses. Drawing inspiration from recent experiments in thin-film lithium-niobate nanophotonics, we present several numerical studies of broadband frequency conversion in chi(2)-nonlinear waveguides. Our analysis provides a detailed understanding of the dynamics and modal structure of quantum noise and entanglement, e.g., in parametric and supercontinuum generation. This talk also surveys some recent results we obtained for harnessing exotic quantum non-Gaussian states of light in ultrafast nonlinear nanophotonics. Proper engineering of these quantum effects may generate entirely new functionalities for nonlinear optics at and beyond the classical-quantum transition.

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U

and

V

, from which reduced second moments, covariance matrices, symplectic eigenvalues, and entropic measures are constructed for arbitrary spectral windows. Applied to soliton-driven resonant radiation, QSSF shows that the selected radiation band acquires a steadily increasing von Neumann entropy and a corresponding loss of purity, quantifying its entanglement with the rest of the spectrum in the lossless Gaussian setting. The analysis also reveals a surprisingly pronounced low-dimensional structure: although the radiation occupies many Fourier bins, its reduced Gaussian state is dominated by only a few Williamson modes. QSSF therefore provides a practical information-theoretic diagnostic for quantum correlations in nonlinear frequency conversion, supercontinuum generation, and multimode squeezed-light formation in ultrafast waveguide platforms.

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χ^{(2)}

nonlinearities, the frameworks developed here are general and are readily extended to the description of dynamical processes based on third-order (

χ^{(3)}

) nonlinearities.