arXiv:2610.31406

Nonlinear quantum noise polarization in macroscopic nonlinear QED

Arman Kashef, Stefan Scheel, Marco Ornigotti

quant-phSubmitted Oct 22, 2026• Announced Oct 23, 2026• 0 citations

Abstract

We construct a quantum theory of light in nonlinearly responding materials with dispersion and absorption and, in particular, show the emergence of non-Gaussian noise associated with nonlinear absorption processes. Our theory is based on a path-integral formulation of the microscopic Huttner-Barnett model including cubic matter self-interaction required for $χ^{(2)}$ nonlinear processes. We show that the noise polarization emerges naturally from a decoupling of the stochastic weights of the bath response which, in case of cubic self-interactions, leads to a decoupling via Airy functions. As the theory is, by construction, consistent with the nonlinear fluctuation-dissipation theorem, it constitutes a viable quantum theory of light in nonlinear media.

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arXiv:2610.31406

Nonlinear quantum noise polarization in macroscopic nonlinear QED

Arman Kashef, Stefan Scheel, Marco Ornigotti

quant-phSubmitted Oct 22, 2026• Announced Oct 23, 2026• 0 citations

arXiv HTML PDF

Abstract

We construct a quantum theory of light in nonlinearly responding materials with dispersion

and absorption and, in particular, show the emergence of non-Gaussian noise associated with

nonlinear absorption processes. Our theory is based on a path-integral formulation of the

microscopic Huttner-Barnett model including cubic matter self-interaction required for

χ^{(2)}

nonlinear processes. We show that the noise polarization emerges naturally from

a decoupling of the stochastic weights of the bath response which, in case of cubic

self-interactions, leads to a decoupling via Airy functions. As the theory is, by

construction, consistent with the nonlinear fluctuation-dissipation theorem, it constitutes

a viable quantum theory of light in nonlinear media.

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Quantum Brownian motion with non-Gaussian noises: Fluctuation-Dissipation Relation and nonlinear Langevin equation

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Building upon the work of Hu, Paz, and Zhang [1,2] on open quantum systems we consider the quantum Brownian motion (QBM) model with one oscillator (position variable $x$ ) as the system, {\it nonlinearly} coupled to an environment of $N$ harmonic oscillators (with mass $m_n$ , natural frequency $ω_n$ , position $q_n$ and momentum $p_n$ variables) in the form $\sum_{n}\left(v_{n1}(x)q_{n}^{k}+v_{n2}(x)p_{n}^{l}\right)$ where $k, l$ are integers (the present work only considers the $k=l=2$ cases). The vertex functions $v_{n1}, v_{n2} $ are of the form $v_{n1}=λC_{n1} f(x), v_{n2}(x)=-λ\,C_{n2}m_{n}^{-2}ω_{n}^{-2}f(x)$ where $C_{n1,2}$ are the coupling constants with the $n$ th oscillator, $f(x)$ is any arbitrary function of $x$ , and $λ$ is a dimensionless constant. Employing the closed-time-path formalism the influence action $S_{IF}$ is calculated using a perturbative expansion in $λ$ . It is possible to identify the terms in $S_{IF}$ quadratic or higher in $Δ(s)\equiv f(x_{+}(s))-f(x_{-}(s))$ to constitute the noise kernel, while terms linear in $Δ$ to that of the dissipation kernel. The non-Gaussian noise kernel gives rise to non-zero three-point correlation function of the corresponding stochastic force. The pathway presented here should be useful for the exploration of \textit{non-Gaussian properties of systems nonlinearly coupled with their environments}; examples in early universe cosmology and in quantum optomechanics (QOM) are mentioned. A modified fluctuation-dissipation relation (FDR) is also established, which ensures the consistency of the model and the accuracy of results even at higher perturbative orders. Another result of significance is the derivation of a nonlinear Langevin equation which is expected to be useful for many open quantum system applications.Building upon the work of Hu, Paz, and Zhang [1,2] on open quantum systems we consider the quantum Brownian motion (QBM) model with one oscillator (position variable $x$) as the system, {\it nonlinearly} coupled to an environment of $N$ harmonic oscillators (with mass $m_n$, natural frequency $ω_n$, position $q_n$ and momentum $p_n$ variables) in the form $\sum_{n}\left(v_{n1}(x)q_{n}^{k}+v_{n2}(x)p_{n}^{l}\right)$ where $k, l$ are integers (the present work only considers the $k=l=2$ cases). The vertex functions $v_{n1}, v_{n2} $ are of the form $v_{n1}=λC_{n1} f(x), v_{n2}(x)=-λ\,C_{n2}m_{n}^{-2}ω_{n}^{-2}f(x)$ where $C_{n1,2}$ are the coupling constants with the $n$th oscillator, $f(x)$ is any arbitrary function of $x$, and $λ$ is a dimensionless constant. Employing the closed-time-path formalism the influence action $S_{IF}$ is calculated using a perturbative expansion in $λ$. It is possible to identify the terms in $S_{IF}$ quadratic or higher in $Δ(s)\equiv f(x_{+}(s))-f(x_{-}(s))$ to constitute the noise kernel, while terms linear in $Δ$ to that of the dissipation kernel. The non-Gaussian noise kernel gives rise to non-zero three-point correlation function of the corresponding stochastic force. The pathway presented here should be useful for the exploration of \textit{non-Gaussian properties of systems nonlinearly coupled with their environments}; examples in early universe cosmology and in quantum optomechanics (QOM) are mentioned. A modified fluctuation-dissipation relation (FDR) is also established, which ensures the consistency of the model and the accuracy of results even at higher perturbative orders. Another result of significance is the derivation of a nonlinear Langevin equation which is expected to be useful for many open quantum system applications.

quant-pharXiv:2602.10421Feb 12, 20260 citations

We construct a quantum theory of light in nonlinearly responding materials with dispersion

and absorption and, in particular, show the emergence of non-Gaussian noise associated with

nonlinear absorption processes. Our theory is based on a path-integral formulation of the

microscopic Huttner-Barnett model including cubic matter self-interaction required for

χ^{(2)}

nonlinear processes. We show that the noise polarization emerges naturally from

a decoupling of the stochastic weights of the bath response which, in case of cubic

self-interactions, leads to a decoupling via Airy functions. As the theory is, by

construction, consistent with the nonlinear fluctuation-dissipation theorem, it constitutes

a viable quantum theory of light in nonlinear media.

Building upon the work of Hu, Paz, and Zhang [1,2] on open quantum systems we consider the quantum Brownian motion (QBM) model with one oscillator (position variable

x

) as the system, {\it nonlinearly} coupled to an environment of

N

harmonic oscillators (with mass

m_n

, natural frequency

ω_n

, position

q_n

and momentum

p_n

variables) in the form

\sum_{n}\left(v_{n1}(x)q_{n}^{k}+v_{n2}(x)p_{n}^{l}\right)

where

k, l

are integers (the present work only considers the

k=l=2

cases). The vertex functions $v_{n1}, v_{n2} $ are of the form

v_{n1}=λC_{n1} f(x), v_{n2}(x)=-λ\,C_{n2}m_{n}^{-2}ω_{n}^{-2}f(x)

where

C_{n1,2}

are the coupling constants with the

n

th oscillator,

f(x)

is any arbitrary function of

x

, and

λ

is a dimensionless constant. Employing the closed-time-path formalism the influence action

S_{IF}

is calculated using a perturbative expansion in

λ

. It is possible to identify the terms in

S_{IF}

quadratic or higher in

Δ(s)\equiv f(x_{+}(s))-f(x_{-}(s))

to constitute the noise kernel, while terms linear in

Δ

to that of the dissipation kernel. The non-Gaussian noise kernel gives rise to non-zero three-point correlation function of the corresponding stochastic force. The pathway presented here should be useful for the exploration of \textit{non-Gaussian properties of systems nonlinearly coupled with their environments}; examples in early universe cosmology and in quantum optomechanics (QOM) are mentioned. A modified fluctuation-dissipation relation (FDR) is also established, which ensures the consistency of the model and the accuracy of results even at higher perturbative orders. Another result of significance is the derivation of a nonlinear Langevin equation which is expected to be useful for many open quantum system applications.