The interaction of a traveling pulse of quantum light with a localized quantum system shows non-Markovian features when scattering takes place in a structured environment. Here, we devise a non-Markovian input-output theory by coherently coupling the scatterer to a pseudomode, which decays into a Markovian reservoir. This incorporates memory effects of a structured environment without altering the cascaded nature of the Lindblad master equation, whose solution provides the quantum state of the output field of any desired mode. We apply our theory to the stimulated emission by a two-level atom, and to transmission of a Gaussian pulse through a cavity. We observe that the non-Markovian revival of coherence in the scatterer distorts the single-mode nature of the incoming pulse, thus resulting in a multimode output field.

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 includes 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.

High-harmonic generation (HHG) in inversion-symmetric systems is typically restricted to odd harmonics by symmetry. Here, we show that this selection rule can be broken without modifying the underlying Hamiltonian. We investigate a boundary-driven Su-Schrieffer-Heeger (SSH) chain coupled to source and sink reservoirs and demonstrate that dissipative dynamics generates a nonequilibrium steady state carrying a finite DC current. While the SSH Hamiltonian retains inversion symmetry, the current-carrying steady-state density matrix does not, leading to the emergence of even harmonics in the emitted spectrum. Using a correlation-matrix approach based on the Lindblad master equation, we obtain the steady state and calculate the resulting HHG response. We find that the intensity of the even harmonics is directly controlled by the transport current, establishing a link between nonequilibrium charge transport and HHG selection rules. Our results uncover a mechanism for even-harmonic generation that relies solely on nonequilibrium steady-state symmetry breaking and provide a route to probing transport currents through ultrafast nonlinear spectroscopy in centrosymmetric quantum systems.

The complex valence band structure of bulk cuprous oxide necessitates going beyond the parabolic approximation to precisely estimate exciton binding energies. The same is true for excitons in cuprous oxide quantum wells, for which many effects have been obtained so far only qualitatively within a hydrogenlike two-band model. Here, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells based on the Luttinger-Kohn model, taking into account the full complex valence band structure. Symmetry properties of the system are discussed. Numerical results based on the diagonalization of the Hamiltonian using B-spline functions reveal the energy shifts and the lifting of degeneracies due to the nondiagonal coupling terms of the complex valence band. The relative oscillator strengths of the excitonic transitions induced by circularly polarized light are also calculated.

We investigate the eigenstates, that is, the wavefunctions of Rydberg excitons in cuprous oxide quantum wells and derive expressions relating them to the oscillator strengths of different exciton states. Using the B-spline expansion, we compute the wavefunctions in coordinate space and estimate the oscillator strengths. The symmetry properties of the states and the non-separability of the wavefunctions are illustrated. Wavefunctions associated with resonances above the scattering threshold, in particular those of bound states in the continuum as well as their partner states, are also given.

Light-matter interaction models invariably rely on the multipole expansion of the electromagnetic potentials generated by complex charge distributions. These multipoles are typically taken to be traceless; however, for a correct evaluation of dispersion forces at all distances, the validity of this assumption has to be checked carefully. Here, we revisit the concept of dispersion forces on an atom near a dielectric surface from the perspective of macroscopic quantum electrodynamics and find that, beyond the quadrupole, the multipoles cannot always be taken as fully traceless. In particular, we show that the trace of the octupole moment contributes to Casimir-Polder interactions beyond the electrostatic regime.

The concept of parity-time symmetry has firmly established non-Hermiticity as a versatile degree of freedom on a variety of physical platforms. In general, the non-Hermitian dynamics of open systems are perceived to be inextricably linked to complex-valued potentials facilitating the local attenuation and coherent amplification in wave mechanics. Along these lines, time reversal symmetry is associated with a complex conjugation of the potential landscape, in essence swapping gain and loss. Here we leverage nonorthogonal coupled-mode theory to synthesize genuinely non-Hermitian dynamics without either gain or loss, and experimentally demonstrate parity-time symmetry via fluorescence measurements in femtosecond-laser-written arrays. Our projective approach allows features of non-Hermiticity to be utilized in scenarios where actual amplification and/or attenuation may disrupt the desired physics, e.g. in nonlinear systems or quantum optics.

We propose a realistic semiconductor system containing bound states in the continuum (BICs) which allows for a practical realization. By varying the confinement strength of excitons in cuprous oxide quantum wells, we show that long-lived Rydberg states of the confined electron-hole pairs appear in the continuum background. The accuracy of calculations of the linewidths based on the coupled-channel Schr & ouml;dinger equation with three channels and only few basis states is confirmed by a numerically exact solution employing a B-spline basis and the complex-coordinate-rotation method. We argue that finite-sized cuprous oxide crystals, due to their large exciton binding energies, are a convenient platform for experimental identification of BICs.

Quantum computation faces a major challenge: the need for stable quantum gates. Holonomies offer a way to increase the stability of quantum gates on a fundamental level, as their functionality directly arises from the geometry of the underlying Hilbert space. We present the quantum optical realization of holonomies as single-qubit quantum gates. Specifically, we implement them in a non-adiabatic scheme, which paves the way for unprecedented miniaturization. To demonstrate their versatility, we realize the Hadamard and Pauli-X gates, experimentally show their non-Abelian nature, and combine them into a single-qubit quantum algorithm, the PQ penny flipover. The planar geometry of our designs enables them to substitute directional couplers currently in widespread use in photonic quantum architectures across all platforms. (c) 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Our conventional understanding of physics is based on the fundamental notion of energy conservation that formally manifests itself in the real-valued energy spectra of Hermitian Hamiltonians. By contrast, so-called open systems can exchange energy with their environment, and, as subsystems of a larger whole, may exhibit non-Hermitian dynamics. Along these lines, non-Hermiticity established by local attenuation and coherent amplification has been firmly established on a variety of platforms. More recently, the related concept of parity-time symmetry has been associated with the wave-mechanical interplay of gain and loss in complex-valued potentials [1], [2]. In the context of quantum systems, however, the presence of actual gain inevitably gives rise to noise, which, in most cases, prevents a direct adaptation of “classical” non-Hermitian settings [3].

Copper monosulfide (CuS), also known as covellite, displays exceptional optoelectronic characteristics, exhibiting both plasmonic and photonic absorption in its monolithic nanomaterial form. It is classified as a hybrid metallic-semiconducting material and a natural hyperbolic material with a distinctive crystal structure. Nanostructured CuS has been demonstrated to support localized surface plasmon resonances (LSPR) in the near-infrared spectral range. Here, the phenomenon of near-infrared (NIR) to visible electromagnetic field localization in ultrathin crystalline quasi-2D CuS nanocrystals is revealed. This is achieved by mapping LSPRs in a range of CuS structures using high-resolution electron energy-loss spectroscopy in combination with cathodoluminescence spectroscopy. In addition to LSPRs, a range of photonic modes in the visible and ultraviolet spectral ranges is identified in colloidally defined single-crystalline nanostructures, with numerical simulations providing supporting evidence. Finally, CuS nanocrystals exhibit visible NIR light emission within the range of 600-900 nm when excited by an electron beam. Altogether, these properties make CuS nanocrystals highly suitable for applications in telecommunications, sensing, and nanophotonics.

The concept of parity-time symmetry has firmly established non-Hermiticity as a versatile degree of freedom on a variety of physical platforms. In general, the non-Hermitian dynamics of open systems are perceived to be inextricably linked to complex-valued potentials facilitating the local attenuation and coherent amplification in wave mechanics. Along these lines, time reversal symmetry is associated with a complex conjugation of the potential landscape, in essence swapping gain and loss. Here we leverage nonorthogonal coupled-mode theory to synthesize genuinely non-Hermitian dynamics without either gain or loss, and experimentally demonstrate parity-time symmetry via fluorescence measurements in femtosecond-laser-written arrays. Our projective approach allows features of non-Hermiticity to be utilized in scenarios where actual amplification and/or attenuation may disrupt the desired physics, e.g. in nonlinear systems or quantum optics. The conventional implementation of parity-time symmetry relies on the interplay of gain and loss. Here, Bentzien et al. present a novel approach towards non-Hermiticity that leverages nonorthogonal modes in coupled waveguides explicitly avoiding the use of either gain or loss.

Light-matter interaction models invariably rely on the multipole expansion of the electromagnetic potentials generated by complex charge distributions. These multipoles are typically taken to be traceless, however, for a correct evaluation of dispersion forces at all distances, the validity of this assumption has to be checked carefully. Here, we revisit the concept of dispersion forces on an atom near a dielectric surface from the perspective of macroscopic quantum electrodynamics and find that, beyond the quadrupole, the multipoles cannot always be taken as fully traceless. In particular, we show that the trace of the octupole moment contributes to Casimir-Polder interactions beyond the electrostatic regime.

To facilitate the transition of quantum effects from the controlled laboratory environment to practical real-world applications, there is a pressing need for scalable platforms. One promising strategy involves integrating thermal vapors with nanostructures designed to manipulate atomic interactions. In this tutorial, we aim to gain deeper insights into this by examining the behavior of thermal vapors that are confined within nanocavities or waveguides and exposed to near-resonant light. We explore the interactions between atoms in confined dense thermal vapors. Our investigation reveals deviations from the predictions of continuous electrodynamics models, including density-dependent line shifts and broadening effects. In particular, our results demonstrate that by carefully controlling the saturation of single atoms and the interactions among multiple atoms using nanostructures, along with controlling the geometry of the atomic cloud, it becomes possible to manipulate the effective optical nonlinearity of the entire atomic ensemble. This capability renders the hybrid thermal atom-nanophotonic platform a distinctive and valuable one for manipulating the collective effect and achieving substantial optical nonlinearities.

One of the most promising nascent technologies, quantum computation faces a major challenge: The need for stable computational building blocks. We present the quantum-optical realization of non-adiabatic holonomies that can be used as single-qubit quantum gates. The hallmark topological protection of non-Abelian geometric phases reduces the need for quantum error correction on a fundamental physical level, while the inherent non-adiabaticity of the structures paves the way for unprecedented miniaturization. To demonstrate their versatility, we realize the Hadamard and Pauli-X gates, experimentally show their non-Abelian nature, and combine them into a single-qubit quantum algorithm, the PQ penny flipover. The planar geometry of such designs enables them to be substituted for the conventional directional coupler meshes currently in wide-spread use in photonic quantum architectures across all platforms.

We identify sequences of concatenated two-mode systems that perform distinct linear optical transformations, whereas their two-photon behavior is invariant under reversal of the order. We experimentally verify this behavior in non-Hermitian interferometers of varying composition.

Due to quantum confinement, excitons in finite-sized crystals behave rather differently than in bulk materials. We investigate the dependence of energies of Rydberg excitons on the strengths of parabolic as well as rectangular confinement potentials in finite-sized crystals. The evolution of the energy levels of hydrogen-like excitons in the crossover region from weak to strong parabolic confinement is analyzed for different quantum numbers by numerical solution of the two-dimensional Schrödinger equation. The energy spectrum of hydrogen-like excitons in Cu$_{2}$O-based rectangular quantum wells is, in turn, obtained numerically from the solution of the three-dimensional Schrödinger equation as a function of the quantum well width. Various crossings and avoided crossings of Rydberg energy levels are observed and categorized based on the symmetry properties of the exciton wave function. Particular attention is paid to the two limiting cases of narrow and wide quantum wells attributed to strong and weak confinement, respectively. The energies obtained with the pure Coulomb interaction are compared with the results originating from the Rytova-Keldysh potential, i.e., by taking into account the dielectric contrast in the quantum well and in the barrier.

In the extreme near-field, when the spatial extension of the atomic wavefunction is no longer negligible compared to the atom-surface distance, the dipole approximation is no longer sufficient to describe Casimir-Polder interactions. Here we calculate the higher-order, quadrupole and octupole, contributions to Casimir-Polder energy shifts of Rydberg atoms close to a dielectric surface. We subsequently investigate the effects of these higher-order terms in thin-cell and selective reflection spectroscopy. Beyond its fundamental interest, this new regime of extremely small atom surface separations is relevant for quantum technology applications with Rydberg or surface-bound atoms interfacing with photonic platforms.