Predicting phenomena that mix few-photon quantum optics with strong field nonlinear optics is hindered by the use of separate theoretical formalisms for each regime. We close this gap with a unified effective field theory valid for frequencies lower than the material-dependent cutoff set by the band gap, plasma frequency, or similar scale. The action couples the electromagnetic gauge field to vector polarisation modes. An isotropic potential generates the optical susceptibilities, while a higher-dimension axion-like term captures magnetoelectric effects; quantisation on the Schwinger-Keldysh contour with doubled BRST ghosts preserves gauge symmetry in dissipative media. One-loop renormalisation-group equations reproduce the measured dispersion of the third-order susceptibility from terahertz to near-visible frequencies after matching a single datum per material. Real-time dynamics solved with a matrix-product-operator engine yield good agreement with published results for GaAs polariton cavities, epsilon-near-zero indium-tin-oxide films and superconducting quarton circuits. The current formulation is limited to these 1-D geometries and sub-cut-off frequencies; higher-dimensional or above-cut-off phenomena will require additional degrees of freedom or numerical methods.
Predicting phenomena that mix few-photon quantum optics with strong field nonlinear optics is hindered by the use of separate theoretical formalisms for each regime. We close this gap with a unified effective field theory valid for frequencies lower than the material-dependent cutoff set by the band gap, plasma frequency, or similar scale. The action couples the electromagnetic gauge field to vector polarisation modes. An isotropic potential generates the optical susceptibilities, while a higher-dimension axion-like term captures magnetoelectric effects; quantisation on the Schwinger-Keldysh contour with doubled BRST ghosts preserves gauge symmetry in dissipative media. One-loop renormalisation-group equations reproduce the measured dispersion of the third-order susceptibility from terahertz to near-visible frequencies after matching a single datum per material. Real-time dynamics solved with a matrix-product-operator engine yield good agreement with published results for GaAs polariton cavities, epsilon-near-zero indium-tin-oxide films and superconducting quarton circuits. The current formulation is limited to these 1-D geometries and sub-cut-off frequencies; higher-dimensional or above-cut-off phenomena will require additional degrees of freedom or numerical methods.
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.
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 loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In structured photonic environments, necessary in practice to achieve strong light-matter coupling, a rigorous model of field quantization within the medium is also needed. Here we use the framework of macroscopic QED by quantizing the fields in an arbitrary material system, with a spatially dependent dispersive and absorptive dielectric, starting from a fundamental light-matter action. We truncate the material and mode degrees of freedom while respecting the gauge principle by imposing a partial gauge-fixing constraint during canonical quantization, which admits a large number of gauges including the Coulomb and multipolar gauges commonly used in quantum optics. We also consider gauge conditions with explicit time dependence, enabling us to unambiguously introduce additional phenomenologically time-dependent light-matter interactions in any gauge. Our results allow one to derive rigorous nonrelativistic models of ultrastrong light-matter interactions in structured photonic environments with no gauge ambiguity. Results for two-level systems and the dipole approximation are discussed, as well as how to go beyond the dipole approximation for effective single-particle models. By comparing with the limiting case of an inhomogeneous dielectric, where dispersion and absorption can be neglected and the fields can be expanded in terms of the generalized transverse eigenfunctions of the dielectric, we show how lossy systems can introduce an additional gauge ambiguity, which we resolve and predict to have fundamental implications for open quantum system models. Finally, we show how observables in mode-truncated systems can be calculated without ambiguity by using a simple gauge-invariant model of photodetection.
Light Propagation: From Atomic to Nuclear Quantim Optics (J Evers et al.) Relativistic High-Order Harmonic Generation (M C Kohler & K Z Hatsagortsyan) Entangled Light and Matter Waves via Non-linear Interactions (M Macovei et al.) Irreversible Photon Transfer in an Ensemble of Λ-Type Atoms and Photon Diode (G Nikoghosyan & M Fleischhauer) Dissipative Chaos in Quantum Distributions (T V Gevorgyan et al.) Frequency Chirped Laser Pulses in Atomic Physics: Coherent Control of Inner and Translational Quantum States (G P Djotyan et al.) Strongly Correlated Quantum Dynamics of Multimode Light Coupled to a Two-Level Atom in a Cavity (T Kumar et al.) Feedback-Driven Adiabatic Quantum Dynamics (A E Allahverdyan & G Mahler) Landau-Zener Transition in Nonlinear Quantum System (A M Ishkhanyan) Photonic and Electronic Phenomena in Structured Media: Multiple Interactions in Multilayered Structures of Nonlinear Materials (D A Antonosyan & G Yu Kryuchkyan) Integrated Photonic Device Structures with Nano-Scale Features: For Sensitive Applications (R M De La Rue) One-, Two-Electronic and Excitonic States in a Quantum Dots with Nontrivial Geometries: Adiabatic Description (K G Dvoyan et al.) Plannar Plasmonic Structures and Non-linear Metal-Dielectric Subwavelength Waveguides (A R Davoyan et al.) Computer Algebra Study of Structural and Symmetry Properties of Discrete Dynamical Systems (V V Kornyak) Exotic Few-Body Bound States in a Lattice (D Petrosyan & M Valiente) Slow Light and Phase Transition in the Array of Atomic Polaritons (I O Barinov et al.) Nonlinear Optical Effects and Spectroscopy: Formation of Narrow Optical Resonances Using Submicron-Thin Atomic Vapor Layers (D Sarkisyan & A Papoyan) Modelling Magneto-Optical Resonances in Atomic Rubidium at D1 Excitation in Extremely Thin Cells While Maintaining a Self-Consistent Set of Theoretical Parameters (L Kalvans et al.) Laser Isotope Separation in Atomic Vapour. Photo-Chemical Method vs Photo-Ionization One (P A Bokhan et al.) Two-Dimensional Confined Terahertz Wave Propagation in Gap Plasmon Waveguide Formed by Two Cyclindrical Surfaces (Yu H Avetisyan et al.) Broadband Similariton: Features and Applications (A Zeytunyan et al.).
A quantum theory of nonlinear phenomena is considered in which account is taken of all contributions from electric and magnetic multipoles, without any multipolar approximation. Exact closed analytical expressions for the multipoles are first obtained from quantum electrodynamics by applying a generalization of the Power-Zienau transformation. The standard procedure is invoked to calculate general electromagnetic susceptibility tensors ${\ensuremath{\chi}}_{\ensuremath{\mu}\ensuremath{\nu}{\ensuremath{\alpha}}_{1}{\ensuremath{\beta}}_{1}\ensuremath{\cdots}{\ensuremath{\alpha}}_{n}{\ensuremath{\beta}}_{n}}^{[n]}$ (${\ensuremath{\omega}}_{1}, \dots{}, {\ensuremath{\omega}}_{n}$). Such a tensor is a shorthand for the electric and magnetic susceptibilities as well as mixed susceptibilities. By considering a relativistic theory based on the Dirac equation, the spin susceptibilities are automatically included. The formalism in this way allows for the computation of a wide range of electro- and magneto-optical effects to any order of perturbation and to any order of multipolar approximation.
Metamaterials are artificially designed materials to exhibit properties not available in natural materials by engineering the constituting elements at sub-wavelength scales, enabling unique interactions of matter with electromagnetic waves or coupling modes of electromagnetic waves. Examples of such novel optics phenomenons include negative index of refraction, cloaking, and super-resolution imaging. The study of superconducting metamaterials operating in the microwave frequency domain has recently generated significant interest in the framework of quantum technologies due to a wide range of direct applications, e.g., exploration of novel quantum optics phenomena, non-destructive quantum sensing, quantum-limited amplification, quantum information processing, and quantum illumination. In contrast to their normal metal and semiconducting counterparts, superconducting metamaterials offer some unique advantages. The most relevant of these for Josephson junction based metamaterials are low losses, flux quantization, and Josephson effects. The Josephson effect in a superconducting loop can also be exploited to exact more control over the nonlinearities of the meta-material.In this thesis, we present Josephson junction based metamaterials with in-situ tunability of second and third-order (Kerr) nonlinearities. We optimized the Josephson junction composites SNAILs, well-known in the superconducting circuits community, for the specific use case of building blocks for an impedance-matched nonlinear meta-material. In such devices, the strong third-order (Kerr) nonlinearity can be tuned from positive to negative values. To demonstrate the efficacy of this phenomenon, we have shown a use case of the meta-material as a TWPA with a new phase-matching mechanism: reversed Kerr phase matching, which utilizes the sign reversal of the Kerr nonlinearity to correct for the dispersion curvature of such devices arising due to its finite plasma. The meta-material operated as reversed Kerr TWPA exhibits up to 4 GHz wide combined amplification band with 8 GHz dynamic band tunability, -98 dBm saturation (1 dB compression point) around 20 dB gain, and amplifier added noise close to the standard quantum limit. The absence of any gaps in the transmission can provide a continuous amplification band with significantly lower gain ripples in contrast to the previously demonstrated TWPAs with dispersion engineering.We also present the generation of entanglement utilizing the metamaterials to demonstrate their versatility and further emphasize their potential in the general framework of nonlinear microwave quantum optics. Due to their large bandwidth, these devices have been identified as promising for generating two-mode squeezing and broadband entanglement. With a device optimized for the generation of broadband entanglement, we observed entanglement between two modes separated by up to 400 MHz. We measured logarithmic negativity between 0.27 and 0.51, and the collective quadrature squeezing below the vacuum limit between 1.5 and 2.1 dB. The presented proof-of-principle results can pave the way towards the implementation of Josephson junction based metamaterials in novel applications, including non-destructive single-photon detection, single-photon measurement and control in c-QED, photon-based quantum computing, precision sensing, the detection of dark matter, and quantum illumination.