Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2609.35146

Nonlinear Quantum Optics in Epsilon-Near-Zero Nanospheres: a Macroscopic Quantum Electrodynamics Approach

Sonia Alipour, Marco Ornigotti

Published Sep 28, 2026• 0 citations
arXivHTMLPDF

Abstract

We present a theoretical framework for handling quantum nonlinear processes in epsilon-near-zero (ENZ_ nano spheres, based on macroscopic quantum electrodynamics and the resonant states (RSs) expansion of the Green's tensor in nano cavities. Using third-harmonic generation (THG) as a case study, we derive analytical expressions for the generation efficiency, and the quantum fluctuations of the generated nonlinear field, as a function of different quantum states of the impinging pump field. Finally, we discuss how to generalise this theoretical framework to arbitrarily quantum nonlinear processes in photonic nanostructures.

DOI
10.48550/arxiv.2609.35146

Related papers

Quantum Theory of Third-harmonic Generation in Epsilon-Near-Zero Materials

Sonia Alipour, Riccardo Franchi, Tornike Shubitidze +3 more

We present a theoretical framework, based on the Green's tensor quantization method, to describe third-harmonic generation in epsilon-near-zero (ENZ) materials and derive analytical, closed-form solutions for the generation efficiency. We validate our model against experimental measurements of wavelength- and angle-resolved third-harmonic generation efficiency from 30 nm-thin ITO nanolayers at low pump intensity, described under the undepleted pump approximation. Our results provide a local and scalar effective model for quantum nonlinear processes in dispersive and lossy ENZ media, and establishes a simple and reliable framework for investigating a variety of nonlinear optical phenomena with applications to quantum sensing, quantum information, and quantum nondemolition measurements.

arXiv:2608.10794•Aug 11, 2026•0 citations

Nonlinear quantum electrodynamics of epsilon-near-zero nanostructures

Luca Dal Negro, Riccardo Franchi, Marco Ornigotti

The authors demonstrate here the nonlinear optical response of epsilon-near-zero (ENZ) nanostructures at the single-photon level using fully nonperturbative quantum theory of open systems with indium tin oxide materials and Kerr-type nonlinearity. Closed-form analytical results obtained for spherical nanoparticles are numerically validated and extended to geometries that can be fabricated using state-of-the-art electron-beam lithography, establishing a rigorous benchmark for understanding quantum nonlinear effects in ENZ nanostructures with optical losses. These results are important to emerging quantum technology, including on-chip single-photon nondemolition detection, sensing, and spectroscopy.

arXiv:2412.20197•Physical review. B./Physical review. B•Oct 15, 2025•3 citations

Effective Quantization of Lossy Nonlinear Epsilon-Near-Zero Media

Avishi Poddar, Jonas von Milczewski, Durdu O. Guney +2 more

In epsilon-near-zero (ENZ) materials, the vanishing real linear permittivity results in the leading-order contribution to the displacement field being nonlinear in the electric field, making conventional canonical quantization approaches highly non-trivial. Existing treatments generally quantize the linear modes first and introduce nonlinear interactions subsequently, an ordering that becomes inadequate in the ENZ regime. Here, we provide, to our knowledge, the first effective single-excitation quantization in which the near-zero linear response, leading nonlinearity, and loss jointly determine the elementary excitation. Using a solvable microscopic atomic system as a theoretical scaffold, we find that this excitation is a polariton: a dressed quasiparticle with partly field and partly material excitations whose coefficients can be parameterized by macroscopic susceptibilities. While this work considers a leading-order $χ^{(3)}$ nonlinearity, the framework could be generalized to include other nonlinear corrections, including a controllable second-order susceptibility $χ^{(2)}$ and systematic higher-order contributions $χ^{(n)}$, $n>2$. Our findings pave the way toward practical applications in quantum photonics, such as single-photon non-demolition detection, by leveraging the strong nonlinearities intrinsic to zero-index materials.

quant-pharXiv:2609.13143•Sep 14, 2026

Causal nonlinear quantum optics

Stefan Scheel, D.‐G. Welsch

We present a quantization scheme for the electromagnetic field in locally responding nonlinear dielectric materials with dispersion and absorption. Based on the Green tensor expansion of the macroscopic electromagnetic field, we derive an expression for the nonlinear polarization that contains, besides the reactive part which is responsible for the nonlinear interaction, a noise contribution that has hitherto been disregarded. For the process of third-harmonic generation, we find that the magnitude of the nonlinear noise polarization is proportional to the intensity of the pump fields.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 24, 2006•13 citations

Nonlinear Meta-Optics

Costantino De Angelis, Luca Carletti, Rocco, D. +6 more

We review the latest advances in the generation of quantum light with nonlinear nanoresonators in metasurfaces, which act both as sources of quantum states and nanoantennas shaping the emitted photons. We outline a general quantum theory of spontaneous photon-pair generation in arbitrary nonlinear photonic structures, including nanoresonators and metasurfaces, which provides an explicit analytical solution for the photon state expressed through the classical Green function. We formulate the correspondence between the quantum photon-pair generation and classical sum-frequency process in nonlinear media, and discuss its application in various contexts, including waveguide circuits and nanostructures. We also discuss the first experimental results demonstrating photon-pair generation in a single nonlinear nanoantenna.

arXiv:2008.11035•CRC Press eBooks•May 21, 2020•13 citations

Macroscopic QED for quantum nanophotonics: emitter-centered modes as a minimal basis for multiemitter problems

Johannes Feist, Antonio I. Fernández‐Domínguez, Francisco José García-Vidal

We present an overview of the framework of macroscopic quantum electrodynamics from a quantum nanophotonics perspective. Particularly, we focus our attention on three aspects of the theory that are crucial for the description of quantum optical phenomena in nanophotonic structures. First, we review the light-matter interaction Hamiltonian itself, with special emphasis on its gauge independence and the minimal and multipolar coupling schemes. Second, we discuss the treatment of the external pumping of quantum optical systems by classical electromagnetic fields. Third, we introduce an exact, complete, and minimal basis for the field quantization in multiemitter configurations, which is based on the socalled emitter-centered modes. Finally, we illustrate this quantization approach in a particular hybrid metallodielectric geometry: two quantum emitters placed in the vicinity of a dimer of Ag nanospheres embedded in a SiN microdisk.

De Gruyter eBooks•May 25, 2021•10 citations
We present a theoretical framework for handling quantum nonlinear processes in epsilon-near-zero (ENZ_ nano spheres, based on macroscopic quantum electrodynamics and the resonant states (RSs) expansion of the Green's tensor in nano cavities. Using third-harmonic generation (THG) as a case study, we derive analytical expressions for the generation efficiency, and the quantum fluctuations of the generated nonlinear field, as a function of different quantum states of the impinging pump field. Finally, we discuss how to generalise this theoretical framework to arbitrarily quantum nonlinear processes in photonic nanostructures.
We present a theoretical framework, based on the Green's tensor quantization method, to describe third-harmonic generation in epsilon-near-zero (ENZ) materials and derive analytical, closed-form solutions for the generation efficiency. We validate our model against experimental measurements of wavelength- and angle-resolved third-harmonic generation efficiency from 30 nm-thin ITO nanolayers at low pump intensity, described under the undepleted pump approximation. Our results provide a local and scalar effective model for quantum nonlinear processes in dispersive and lossy ENZ media, and establishes a simple and reliable framework for investigating a variety of nonlinear optical phenomena with applications to quantum sensing, quantum information, and quantum nondemolition measurements.
The authors demonstrate here the nonlinear optical response of epsilon-near-zero (ENZ) nanostructures at the single-photon level using fully nonperturbative quantum theory of open systems with indium tin oxide materials and Kerr-type nonlinearity. Closed-form analytical results obtained for spherical nanoparticles are numerically validated and extended to geometries that can be fabricated using state-of-the-art electron-beam lithography, establishing a rigorous benchmark for understanding quantum nonlinear effects in ENZ nanostructures with optical losses. These results are important to emerging quantum technology, including on-chip single-photon nondemolition detection, sensing, and spectroscopy.
In epsilon-near-zero (ENZ) materials, the vanishing real linear permittivity results in the leading-order contribution to the displacement field being nonlinear in the electric field, making conventional canonical quantization approaches highly non-trivial. Existing treatments generally quantize the linear modes first and introduce nonlinear interactions subsequently, an ordering that becomes inadequate in the ENZ regime. Here, we provide, to our knowledge, the first effective single-excitation quantization in which the near-zero linear response, leading nonlinearity, and loss jointly determine the elementary excitation. Using a solvable microscopic atomic system as a theoretical scaffold, we find that this excitation is a polariton: a dressed quasiparticle with partly field and partly material excitations whose coefficients can be parameterized by macroscopic susceptibilities. While this work considers a leading-order χ(3)χ^{(3)}χ(3) nonlinearity, the framework could be generalized to include other nonlinear corrections, including a controllable second-order susceptibility χ(2)χ^{(2)}χ(2) and systematic higher-order contributions χ(n)χ^{(n)}χ(n), n>2n>2n>2. Our findings pave the way toward practical applications in quantum photonics, such as single-photon non-demolition detection, by leveraging the strong nonlinearities intrinsic to zero-index materials.
We present a quantization scheme for the electromagnetic field in locally responding nonlinear dielectric materials with dispersion and absorption. Based on the Green tensor expansion of the macroscopic electromagnetic field, we derive an expression for the nonlinear polarization that contains, besides the reactive part which is responsible for the nonlinear interaction, a noise contribution that has hitherto been disregarded. For the process of third-harmonic generation, we find that the magnitude of the nonlinear noise polarization is proportional to the intensity of the pump fields.
We review the latest advances in the generation of quantum light with nonlinear nanoresonators in metasurfaces, which act both as sources of quantum states and nanoantennas shaping the emitted photons. We outline a general quantum theory of spontaneous photon-pair generation in arbitrary nonlinear photonic structures, including nanoresonators and metasurfaces, which provides an explicit analytical solution for the photon state expressed through the classical Green function. We formulate the correspondence between the quantum photon-pair generation and classical sum-frequency process in nonlinear media, and discuss its application in various contexts, including waveguide circuits and nanostructures. We also discuss the first experimental results demonstrating photon-pair generation in a single nonlinear nanoantenna.
We present an overview of the framework of macroscopic quantum electrodynamics from a quantum nanophotonics perspective. Particularly, we focus our attention on three aspects of the theory that are crucial for the description of quantum optical phenomena in nanophotonic structures. First, we review the light-matter interaction Hamiltonian itself, with special emphasis on its gauge independence and the minimal and multipolar coupling schemes. Second, we discuss the treatment of the external pumping of quantum optical systems by classical electromagnetic fields. Third, we introduce an exact, complete, and minimal basis for the field quantization in multiemitter configurations, which is based on the socalled emitter-centered modes. Finally, we illustrate this quantization approach in a particular hybrid metallodielectric geometry: two quantum emitters placed in the vicinity of a dimer of Ag nanospheres embedded in a SiN microdisk.