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Physical Review Letters

Quantum Noise in Fibers with Arbitrary Nonlinear Profiles

J. Bonetti, D. F. Grosz, S. M. Hernández

Published May 26, 2021• 5 citations
Publisher

Abstract

In this Letter we introduce a novel equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles. To the best of our knowledge, such an endeavor has not been undertaken before despite the growing relevance of fiber optics in the design of new quantum devices. We show that the stochastic generalized nonlinear Schrödinger equation, derived from a quantum theory of optical fibers, leads to unphysical results such as a negative photon number and the appearance of a dominant anti-Stokes sideband when applied to this kind of waveguides. Starting from a recently introduced master-equation approach to propagation in fibers, we derive a novel stochastic photon-conserving nonlinear Schrödinger equation suitable for modeling arbitrary nonlinear profiles, thus greatly enhancing the study of fiber-based quantum devices.

DOI
10.1103/physrevlett.126.213602

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In this Letter we introduce a novel equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles. To the best of our knowledge, such an endeavor has not been undertaken before despite the growing relevance of fiber optics in the design of new quantum devices. We show that the stochastic generalized nonlinear Schrödinger equation, derived from a quantum theory of optical fibers, leads to unphysical results such as a negative photon number and the appearance of a dominant anti-Stokes sideband when applied to this kind of waveguides. Starting from a recently introduced master-equation approach to propagation in fibers, we derive a novel stochastic photon-conserving nonlinear Schrödinger equation suitable for modeling arbitrary nonlinear profiles, thus greatly enhancing the study of fiber-based quantum devices.
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We put forth an approach to obtain a quantum master equation for the propagation of light in nonlinear fiber optics by relying on simple quantum pictures of the processes (linear and nonlinear) occurring along propagation in an optical fiber. This equation is shown to be in excellent agreement with the classical Generalized Nonlinear Schrodinger Equation and predicts the effects of self-steepening and spontaneous Raman scattering. Last, we apply these results to the analysis of two cases of relevance in quantum technologies: single-photon frequency translation and spontaneous four-wave mixing.
We analyze the quantum dynamics of radiation propagating in a single-mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or +P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fiber-optics communications, networking, and sensor technology.
In this Letter, we revisit the quantum theory of propagation in nonlinear fibers. Unlike previous works, we present an effective propagation equation for the reduced density matrix of the complex envelope of the electric field. This original proposal is shown to be in agreement with the theory of quantum noise in fibers and puts forth a powerful tool for the study of fiber-based quantum devices. To underscore its applicability, we analyze the performance of a heralded single-photon scheme in terms of probabilities, an approach that conveniently lends itself to the optimization of such sources.
We analyze the quantum dynamics of radiation propagating in a single-mode optical fibre with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum-noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This treatment allows quantum Langevin equations, which have a classical form except for additional quantum-noise terms, to be calculated. In practical calculations, it is more useful to transform to Wigner or +P quasi-probability operator representations. These transformations result in stochastic equations that can be analyzed by use of perturbation theory or exact numerical techniques. The results have applications to fibre-optics communications, networking, and sensor technology.
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