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arXiv:2412.20197 · Physical review. B./Physical review. B

Nonlinear quantum electrodynamics of epsilon-near-zero nanostructures

Luca Dal Negro, Riccardo Franchi, Marco Ornigotti

Published Oct 15, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/9yyx-s3m9

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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.
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.
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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 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.
Quantum nonlinear optics seeks to harness strong photon-photon interactions for scalable quantum technologies, although dissipative losses still pose a major barrier to near-unity conversion efficiency. Here, we bridge non-Hermitian physics with the quantum nonlinear domain by exploiting perfect absorption to identify and optimize few-photon nonlinear processes. We theoretically investigate two circuit QED systems, operating in the light-matter ultrastrong coupling regime. The first (i) enables simultaneous two-atom excitations by single photons, while the second (ii) realizes the strong coupling between a single-photon and a two-photon Fock states. We demonstrate that, since the strong optical nonlinearities cause quantum spectral features to emerge already at the level of linear response theory, the perfect absorption condition in ∣S11∣|S_{11}|∣S11​∣ enables near-deterministic single-photon down-conversion into (i) a qubit-qubit-correlated pair and (ii) a two-photon pair. We show that the conversion efficiency can be systematically optimized through experimentally accessible parameters, both linked to the emergence of Hermitian subspaces within the effective non-Hermitian Hamiltonians. These findings position non-Hermitian engineering as a broadly applicable route to optimizing quantum devices at the single-photon level, even beyond circuit-QED platforms.
We employ a quantum theory of the nonlinear optical response from an actual solid-state material possessing an intrinsic bulk contribution to the third-order nonlinear susceptibility (Kerr-type nonlinearity), which can be arbitrarily nanostructured to achieve diffraction-limited electro-magnetic-field confinement. By calculating the zero-time-delay second-order correlation of the cavity field, we set the conditions for using semiconductor or insulating materials with near-infrared energy gaps as an efficient means to obtain single-photon nonlinear behavior in prospective solid-state integrated devices, alternative to ideal sources of quantum radiation such as, e.g., single two-level emitters.