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.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.

quant-pharXiv:2610.31406Oct 23, 20260 citations

Quantum theory of light in nonlinear media with dispersion and absorption

Eduard Schmidt, John Jeffers, Stephen Mark Barnett +2 more

We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We start from a microscopic model and apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field, with special emphasis on the propagation of quantum-light pulses in Kerr media. In particular, the method enables us to derive systematically the noise sources that arise naturally in the nonlinear terms.We present a canonical quantum theory of radiation in nonlinear media taking into account the effects of linear dispersion and absorption in a consistent way. We start from a microscopic model and apply recently developed concepts of the quantization of radiation in dispersive and absorbing linear media and extend the theory in order to include nonlinear optical processes. We derive propagation equations in space and time for the quantized radiation field, with special emphasis on the propagation of quantum-light pulses in Kerr media. In particular, the method enables us to derive systematically the noise sources that arise naturally in the nonlinear terms.

Journal of Modern OpticsFeb 1, 199816 citations

Path integral quantization of the electromagnetic field in nonlinear dielectric materials

Arman Kashef, Oscar Perearnau Herrero, Alexander Szameit +2 more

We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response. Quantization is performed by constructing an effective action in a path-integral formalism by integrating out matter and bath degrees of freedom. We show how a nonlinear response function associated with Kerr nonlinearity is obtained through the model and, after full field quantization, we derive the Feynman rules from this theory.We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response. Quantization is performed by constructing an effective action in a path-integral formalism by integrating out matter and bath degrees of freedom. We show how a nonlinear response function associated with Kerr nonlinearity is obtained through the model and, after full field quantization, we derive the Feynman rules from this theory.

quant-pharXiv:2605.03836Physical Review AMay 6, 20260 citations

ON THE QUANTUM THEORY OF NONLINEAR OPTICS

Mark S. Hillery, Leonard D. Mlodinow

Jan 1, 19831 citation

A Quantum Theory of Optical Dispersion

C. G. DARWIN

NatureDec 1, 192216 citations

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.