Quantization of Quasinormal Modes for Open Cavities and Plasmonic Cavity Quantum Electrodynamics

Quantum engineering of the radiative properties of a nanoscale mesoscopic system

Despite the recent advances in quantum technology, the problem of controlling the light emission properties of quantum emitters used in numerous applications remains: a large spectral width, low intensity, blinking, photodegradation, biocompatibility, etc. In this work, we present the theoretical and experimental investigation of quantum light sources - mesoscopic systems consisting of fluorescent molecules in a thin polydopamine layer coupled with metallic or dielectric nanoparticles. Polydopamines possess many attractive adhesive and optical properties that promise their use as host media for dye molecules. However, numerous attempts to incorporate fluorescent molecules into polydopamines have failed, as polydopamine has been shown to be a very efficient fluorescence quencher through Förster resonance energy transfer and/or photoinduced electron transfer. Using the system as an example, we demonstrate new insights into the interactions between molecules and electromagnetic fields by carefully shaping its energy levels through strong matter-wave coupling of molecules to metallic nanoparticles. We show that the strong coupling effectively suppresses the quenching of fluorescent molecules in polydopamine, opening new possibilities for imaging.

Toward Optimum Coupling between Free Electrons and Confined Optical Modes

Free electrons are excellent tools to probe and manipulate nanoscale optical fields with emerging applications in ultrafast spectromicroscopy and quantum metrology. However, advances in this field are hindered by the small probability associated with the excitation of single optical modes by individual free electrons. Here, we theoretically investigate the scaling properties of the electron-driven excitation probability for a wide variety of optical modes including plasmons in metallic nanostructures and Mie resonances in dielectric cavities, spanning a broad spectral range that extends from the ultraviolet to the infrared region. The highest probabilities for the direct generation of three-dimensionally confined modes are observed at low electron and mode energies in small structures, with order-unity (∼100%) coupling demanding the use of <100 eV electrons interacting with eV polaritons confined down to tens of nanometers in space. Electronic transitions in artificial atoms also emerge as practical systems to realize strong coupling to few-eV free electrons. In contrast, conventional dielectric cavities reach a maximum probability in the few-percent range. In addition, we show that waveguide modes can be generated with higher-than-unity efficiency by phase-matched interaction with grazing electrons, suggesting a practical method to create multiple excitations of a localized optical mode by an individual electron through funneling the so-generated propagating photons into a confining cavity─an alternative approach to direct electron-cavity interaction. Our work provides a roadmap to optimize electron-photon coupling with potential applications in electron spectromicroscopy as well as nonlinear and quantum optics at the nanoscale.

Strong Coupling of Two-Dimensional Excitons and Plasmonic Photonic Crystals: Microscopic Theory Reveals Triplet Spectra

Monolayers of transition metal dichalcogenides (TMDCs) are direct-gap semiconductors with strong light-matter interactions featuring tightly bound excitons, while plasmonic crystals (PCs), consisting of metal nanoparticles that act as meta-atoms, exhibit collective plasmon modes and allow one to tailor electric fields on the nanoscale. Recent experiments show that TMDC-PC hybrids can reach the strong-coupling limit between excitons and plasmons, forming new quasiparticles, so-called plexcitons. To describe this coupling theoretically, we develop a self-consistent Maxwell-Bloch theory for TMDC-PC hybrid structures, which allows us to compute the scattered light in the near- and far-fields explicitly and provide guidance for experimental studies. One of the key findings of the developed theory is the necessity to differentiate between bright and originally momentum-dark excitons. Our calculations reveal a spectral splitting signature of strong coupling of more than 100 meV in gold-MoSe2 structures with 30 nm nanoparticles, manifesting in a hybridization of the plasmon mode with momentum-dark excitons into two effective plexcitonic bands. The semianalytical theory allows us to directly infer the characteristic asymmetric line shape of the hybrid spectra in the strong coupling regime from the energy distribution of the momentum-dark excitons. In addition to the hybridized states, we find a remaining excitonic mode with significantly smaller coupling to the plasmonic near-field, emitting directly into the far-field. Thus, hybrid spectra in the strong coupling regime can contain three emission peaks.

Efficient method for modeling large-scale arrays of optical nanoresonators based on the coupling theory of quasinormal mode

We propose an efficient method for calculating the electromagnetic field of a large-scale array of optical nanoresonators based on the coupling theory of quasinormal mode (QNM). In this method, two approaches of the scattered-field reconstruction and stationary-phase-principle calculated plane-wave expansion are developed to obtain the regularized QNM (RQNM) in different regions. This accurate and efficient calculation of RQNM resolves the far-field divergence issue of QNMs in the QNM-coupling theory, thus enabling a rapid computation of the electromagnetic field of a large-scale array of optical nanoresonators, which is a challenging task for full-wave numerical methods. Using this method, we consider the numerical example of the radiation problem of a single point source in a large-scale periodic array of optical nanoantennas. In comparison to full-wave numerical methods, this method significantly reduces the computation time by 1∼2 orders of magnitude while maintaining accuracy. The high computational efficiency and physical intuitiveness of the method enables to clarify the impact of array size (exceeding 50 × 50 wavelengths), period and field-coupling range (far beyond the tight-binding approximation) on the optical response. The proposed method and results can provide an efficient tool and guidance for the design of large-scale arrays of optical nanoresonators.

Photonic Flatband Resonances in Multiple Light Scattering

We introduce the concept of photonic flatband resonances and demonstrate it for an array of high-index dielectric particles. We employ the multiple Mie scattering theory and demonstrate that both short- and long-range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both near- and far-field characteristics, we uncover how the flatbands emerge due to a fine tuning of resonators' radiation fields, and predict that hybridization of a flatband resonance with an electric hot spot can lead to giant values of the Purcell factor for the electric dipolar emitters.

Ab Initio Calculations of Quantum Light-Matter Interactions in General Electromagnetic Environments

The emerging field of strongly coupled light-matter systems has drawn significant attention in recent years because of the prospect of altering both the physical and chemical properties of molecules and materials. Because this emerging field draws on ideas from both condensed-matter physics and quantum optics, it has attracted the attention of theoreticians from both fields. While the former often employ accurate descriptions of the electronic structure of the matter, the description of the electromagnetic environment is often oversimplified. In contrast, the latter often employs sophisticated descriptions of the electromagnetic environment while using oversimplified few-level approximations of the electronic structure. Both approaches are problematic because the oversimplified descriptions of the electronic system are incapable of describing effects such as light-induced structural changes in the electronic system, while the oversimplified descriptions of the electromagnetic environments can lead to unphysical predictions because the light-matter interactions strengths are misrepresented. In this work, we overcome these shortcomings and present the first method which can quantitatively describe both the electronic system and general electromagnetic environments from first principles. We realize this by combining macroscopic QED (MQED) with Quantum Electrodynamical Density-Functional Theory. To exemplify this approach, we consider the example of an absorbing spherical cavity and study the impact of different parameters of both the environment and the electronic system on the transition from weak-to-strong coupling for different aromatic molecules. As part of this work, we also provide an easy-to-use tool to calculate the cavity coupling strengths for simple cavity setups. Our work is a significant step toward parameter-free ab initio calculations for strongly coupled quantum light-matter systems and will help bridge the gap between theoretical methods and experiments in the field.

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

The Rise and Current Status of Polaritonic Photochemistry and Photophysics

The interaction between molecular electronic transitions and electromagnetic fields can be enlarged to the point where distinct hybrid light-matter states, polaritons, emerge. The photonic contribution to these states results in increased complexity as well as an opening to modify the photophysics and photochemistry beyond what normally can be seen in organic molecules. It is today evident that polaritons offer opportunities for molecular photochemistry and photophysics, which has caused an ever-rising interest in the field. Focusing on the experimental landmarks, this review takes its reader from the advent of the field of polaritonic chemistry, over the split into polariton chemistry and photochemistry, to present day status within polaritonic photochemistry and photophysics. To introduce the field, the review starts with a general description of light-matter interactions, how to enhance these, and what characterizes the coupling strength. Then the photochemistry and photophysics of strongly coupled systems using Fabry-Perot and plasmonic cavities are described. This is followed by a description of room-temperature Bose-Einstein condensation/polariton lasing in polaritonic systems. The review ends with a discussion on the benefits, limitations, and future developments of strong exciton-photon coupling using organic molecules.

Certifying Multimode Light-Matter Interaction in Lossy Resonators

Quantum models based on few-mode master equations have been a central tool in the study of resonator quantum electrodynamics, extending the seminal single-mode Jaynes-Cummings model to include loss and multiple modes. Despite their broad application range, previous approaches within this framework have either relied on a Markov approximation or a fitting procedure. By combining ideas from pseudomode and quasinormal mode theory, we develop a certification criterion for multi-mode effects in lossy resonators. It is based on a witness observable, and neither requires a fitting procedure nor a Markov approximation. Using the resulting criterion, we demonstrate that such multi-mode effects are important for understanding previous experiments in x-ray cavity QED with Mössbauer nuclei and that they allow one to tune the nuclear ensemble properties.

Non-Hermitian Anharmonicity Induces Single-Photon Emission

Single-photon sources are in high demand for quantum information applications. A paradigmatic way to achieve single-photon emission is through anharmonicity in the energy levels, such that the absorption of a single photon from a coherent drive shifts the system out of resonance and prevents absorption of a second one. We identify a novel mechanism for single-photon emission through non-Hermitian anharmonicity, i.e., anharmonicity in the losses instead of in the energy levels. We demonstrate the mechanism in two types of systems, including a feasible setup consisting of a hybrid metallodielectric cavity weakly coupled to a two-level emitter, and show that it induces high-purity single-photon emission at high repetition rates.

Anomalous spontaneous emission dynamics at chiral exceptional points

An open quantum system operated at the spectral singularities where dimensionality reduces, known as exceptional points (EPs), demonstrates distinguishing behavior from the Hermitian counterpart. Here, we present an analytical description of local density of states (LDOS) for microcavity featuring chiral EPs, and unveil the anomalous spontaneous emission dynamics from a quantum emitter (QE) due to the non-Lorentzian response of EPs. Specifically, we reveal that a squared Lorentzian term of LDOS contributed by chiral EPs can destructively interfere with the linear Lorentzian profile, resulting in the null Purcell enhancement to a QE with special transition frequency, which we call EP induced transparency. While for the case of constructive interference, the squared Lorentzian term can narrow the linewidth of Rabi splitting even below that of bare components, and thus significantly suppresses the decay of Rabi oscillation. Interestingly, we further find that an open microcavity with chiral EPs supports atom-photon bound states for population trapping and decay suppression in long-time dynamics. As applications, we demonstrate the advantages of microcavity operated at chiral EPs in achieving high-fidelity entanglement generation and high-efficiency single-photon generation. Our work unveils the exotic cavity quantum electrodynamics unique to chiral EPs, which opens the door for controlling light-matter interaction at the quantum level through non-Hermiticity, and holds great potential in building high-performance quantum-optics devices.

Quasinormal Mode Expansion Theory for Mesoscale Plasmonic Nanoresonators: An Analytical Treatment of Nonclassical Electromagnetic Boundary Condition

Nonclassical quantum effects will significantly affect the optical response of plasmonic nanoresonators with mesoscale feature sizes between about 2 and 20 nm, and can be fully described by the nonclassical electromagnetic boundary condition (NEBC) expressed with the surface-response Feibelman d parameters. In this Letter, a quasinormal mode (QNM) expansion theory under the NEBC is proposed. By adopting the easily solved classical QNMs under the classical electromagnetic boundary condition as a complete set of basis functions, rigorous expansions of the nonclassical source-free QNMs and source-excited electromagnetic field under the nonperturbative NEBC are provided. With the obtained nonclassical QNMs as basis functions, expansions of the nonclassical source-excited field and Green's function tensor are further obtained. These expansions have a fully analytical dependence on the NEBC and classical QNMs, thus transparently unveiling their impact on the nonclassical QNMs and source-excited electromagnetic field. For instance, a new expression of mode volume is proposed for analyzing the nonclassically corrected Purcell factor. The proposed theory is physically intuitive and computationally efficient which is enabled by the dominance of a small set of classical QNMs, thus providing an efficient tool for understanding and designing mesoscale plasmonic nanoresonators.

Cavity spectral-hole-burning to boost coherence in plasmon-emitter strong coupling systems

Significant decoherence of the plasmon-emitter (i.e., plexcitonic) strong coupling systems hinders the progress towards their applications in quantum technology due to the unavoidable lossy nature of the plasmons. Inspired by the concept of spectral-hole-burning (SHB) for frequency-selective bleaching of the emitter ensemble, we propose 'cavity SHB' by introducing cavity modes with moderate quality factors to the plexcitonic system to boost its coherence. We show that the detuning of the introduced cavity mode with respect to the original plexcitonic system, which defines the location of the cavity SHB, is the most critical parameter. Simultaneously introducing two cavity modes of opposite detunings, the excited-state population of the emitter can be enhanced by 4.5 orders of magnitude within 300 fs, and the attenuation of the emitter's population can be slowed down by about 56 times. This theoretical proposal provides a new approach of cavity engineering to enhance the plasmon-emitter strong coupling systems' coherence, which is important for realistic hybrid-cavity design for applications in quantum technology.

Few-mode field quantization for multiple emitters

The control of the interaction between quantum emitters using nanophotonic structures holds great promise for quantum technology applications, while its theoretical description for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes form a high-dimensional continuum. We here introduce an approach that permits a quantized description of the full EM field through a small number of discrete modes. This extends the previous work in ref. (I. Medina, F. J. García-Vidal, A. I. Fernández-Domínguez, and J. Feist, "Few-mode field quantization of arbitrary electromagnetic spectral densities," Phys. Rev. Lett., vol. 126, p. 093601, 2021) to the case of an arbitrary number of emitters, without any restrictions on the emitter level structure or dipole operators. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. We illustrate the power of our approach for a system of three emitters placed within a hybrid metallodielectric photonic structure and show that excitation transfer is highly sensitive to the properties of the hybrid photonic-plasmonic modes.

Efficient Quadrature Squeezing from Biexcitonic Parametric Gain in Atomically Thin Semiconductors

Modification of electromagnetic quantum fluctuations in the form of quadrature squeezing is a central quantum resource, which can be generated from nonlinear optical processes. Such a process is facilitated by coherent two-photon excitation of the strongly bound biexciton in atomically thin semiconductors. We show theoretically that interfacing an atomically thin semiconductor with an optical cavity makes it possible to harness this two-photon resonance and use the biexcitonic parametric gain to generate squeezed light with input power an order of magnitude below current state-of-the-art devices with conventional third-order nonlinear materials that rely on far off-resonant nonlinearities. Furthermore, the squeezing bandwidth is found to be in the range of several meV. These results identify atomically thin semiconductors as a promising candidate for on-chip squeezed-light sources.

A Theoretical Perspective on Molecular Polaritonics

In the past decade, much theoretical research has focused on studying the strong coupling between organic molecules (or quantum emitters, in general) and light modes. The description and prediction of polaritonic phenomena emerging in this light-matter interaction regime have proven to be difficult tasks. The challenge originates from the enormous number of degrees of freedom that need to be taken into account, both in the organic molecules and in their photonic environment. On one hand, the accurate treatment of the vibrational spectrum of the former is key, and simplified quantum models are not valid in many cases. On the other hand, most photonic setups have complex geometric and material characteristics, with the result that photon fields corresponding to more than just a single electromagnetic mode contribute to the light-matter interaction in these platforms. Moreover, loss and dissipation, in the form of absorption or radiation, must also be included in the theoretical description of polaritons. Here, we review and offer our own perspective on some of the work recently done in the modeling of interacting molecular and optical states with increasing complexity.

Linear response theory of open systems with exceptional points

Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M_s with M_s = 2, 3, …, M, depending on the choice of input and output channels.

The authors develop a closed-form expansion of the linear response associated with resonant non-Hermitian systems having exceptional points and demonstrate that the spectral response may involve different super Lorentzian lineshapes depending on the input/output channel configuration.

Enhanced TEMPO Algorithm for Quantum Path Integrals with Off-Diagonal System-Bath Coupling: Applications to Photonic Quantum Networks

Multitime system correlation functions are relevant in various areas of physics and science, dealing with system-bath interaction including spectroscopy and quantum optics, where many of these schemes include an off-diagonal system bath interaction. Here we extend the enhanced time-evolving matrix product operator (eTEMPO) algorithm for quantum path integrals using tensor networks [Phys. Rev. Lett. 123, 240602 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.240602 to open quantum systems with off-diagonal coupling beyond a single two level system. We exemplify the approach on a coupled cavity waveguide system with spatially separated quantum two-state emitters, though many other applications in material science are possible, including entangled photon propagation, photosynthesis spectroscopy, and on-chip quantum optics with realistic dissipation.

Theoretical Challenges in Polaritonic Chemistry

Polaritonic chemistry exploits strong light-matter coupling between molecules and confined electromagnetic field modes to enable new chemical reactivities. In systems displaying this functionality, the choice of the cavity determines both the confinement of the electromagnetic field and the number of molecules that are involved in the process. While in wavelength-scale optical cavities the light-matter interaction is ruled by collective effects, plasmonic subwavelength nanocavities allow even single molecules to reach strong coupling. Due to these very distinct situations, a multiscale theoretical toolbox is then required to explore the rich phenomenology of polaritonic chemistry. Within this framework, each component of the system (molecules and electromagnetic modes) needs to be treated in sufficient detail to obtain reliable results. Starting from the very general aspects of light-molecule interactions in typical experimental setups, we underline the basic concepts that should be taken into account when operating in this new area of research. Building on these considerations, we then provide a map of the theoretical tools already available to tackle chemical applications of molecular polaritons at different scales. Throughout the discussion, we draw attention to both the successes and the challenges still ahead in the theoretical description of polaritonic chemistry.

Shortcut to Self-Consistent Light-Matter Interaction and Realistic Spectra from First Principles

We introduce a simple approach to how an electromagnetic environment can be efficiently embedded into state-of-the-art electronic structure methods, taking the form of radiation-reaction forces. We demonstrate that this self-consistently provides access to radiative emission, natural linewidth, Lamb shifts, strong coupling, electromagnetically induced transparency, Purcell-enhanced and superradiant emission. As an example, we illustrate its seamless integration into time-dependent density-functional theory with virtually no additional cost, presenting a convenient shortcut to light-matter interactions.

Plexcitonic Quantum Light Emission from Nanoparticle-on-Mirror Cavities

We investigate the quantum-optical properties of the light emitted by a nanoparticle-on-mirror cavity filled with a single quantum emitter. Inspired by recent experiments, we model a dark-field setup and explore the photon statistics of the scattered light under grazing laser illumination. Exploiting analytical solutions to Maxwell's equations, we quantize the nanophotonic cavity fields and describe the formation of plasmon-exciton polaritons (or plexcitons) in the system. This way, we reveal that the rich plasmonic spectrum of the nanocavity offers unexplored mechanisms for nonclassical light generation that are more efficient than the resonant interaction between the emitter natural transition and the brightest optical mode. Specifically, we find three different sample configurations in which strongly antibunched light is produced. Finally, we illustrate the power of our approach by showing that the introduction of a second emitter in the platform can enhance photon correlations further.

Ultrastrong Coupling of a Single Molecule to a Plasmonic Nanocavity: A First-Principles Study

Ultrastrong coupling (USC) is a distinct regime of light-matter interaction in which the coupling strength is comparable to the resonance energy of the cavity or emitter. In the USC regime, common approximations to quantum optical Hamiltonians, such as the rotating wave approximation, break down as the ground state of the coupled system gains photonic character due to admixing of vacuum states with higher excited states, leading to ground-state energy changes. USC is usually achieved by collective coherent coupling of many quantum emitters to a single mode cavity, whereas USC with a single molecule remains challenging. Here, we show by time-dependent density functional theory (TDDFT) calculations that a single organic molecule can reach USC with a plasmonic dimer, consisting of a few hundred atoms. In this context, we discuss the capacity of TDDFT to represent strong coupling and its connection to the quantum optical Hamiltonian. We find that USC leads to appreciable ground-state energy modifications accounting for a non-negligible part of the total interaction energy, comparable to k _B T at room temperature.

Exact solution of polaritonic systems with arbitrary light and matter frequency-dependent losses

In this paper, we perform the exact diagonalization of a light–matter strongly coupled system taking into account arbitrary losses via both energy dissipation in the optically active material and photon escape out of the resonator. This allows us to naturally treat the cases of couplings with structured reservoirs, which can strongly impact the polaritonic response via frequency-dependent losses or discrete-to-continuum strong coupling. We discuss the emergent gauge freedom of the resulting theory and provide analytical expressions for all the gauge-invariant observables in both the Power–Zienau–Woolley and the Coulomb representations. In order to exemplify the results, the theory is finally specialized to two specific cases. In the first one, both light and matter resonances are characterized by Lorentzian linewidths, and in the second one, a fixed absorption band is also present. The analytical expressions derived in this paper can be used to predict, fit, and interpret results from polaritonic experiments with arbitrary values of the light–matter coupling and with losses of arbitrary intensity and spectral shape in both the light and matter channels. A Matlab code implementing our results is provided.

Normalization, orthogonality, and completeness of quasinormal modes of open systems: the case of electromagnetism [Invited]

The scattering of electromagnetic waves by resonant systems is determined by the excitation of the quasinormal modes (QNMs), i.e. the eigenmodes, of the system. This Review addresses three fundamental concepts in relation to the representation of the scattered field as a superposition of the excited QNMs: normalization, orthogonality, and completeness. Orthogonality and normalization enable a straightforward assessment of the QNM excitation strength for any incident wave. Completeness guarantees that the scattered field can be faithfully expanded into the complete QNM basis. These concepts are not trivial for non-conservative (non-Hermitian) systems and have driven many theoretical developments since initial studies in the 70's. Yet, they are not easy to grasp from the extensive and scattered literature, especially for newcomers in the field. After recalling fundamental results obtained in initial studies on the completeness of the QNM basis for simple resonant systems, we review recent achievements and the debate on the normalization, clarify under which circumstances the QNM basis is complete, and highlight the concept of QNM regularization with complex coordinate transforms.

General Framework of Canonical Quasinormal Mode Analysis for Extreme Nano-optics

Optical phenomena associated with an extremely localized field should be understood with considerations of nonlocal and quantum effects, which pose a hurdle to conceptualize the physics with a picture of eigenmodes. Here we first propose a generalized Lorentz model to describe general nonlocal media under linear mean-field approximation and formulate source-free Maxwell's equations as a linear eigenvalue problem to define the quasinormal modes. Then we introduce an orthonormalization scheme for the modes and establish a canonical quasinormal mode framework for general nonlocal media. Explicit formalisms for metals described by a quantum hydrodynamic model and polar dielectrics with nonlocal response are exemplified. The framework enables for the first time a direct modal analysis of mode transition in the quantum tunneling regime and provides physical insights beyond usual far-field spectroscopic analysis. Applied to nonlocal polar dielectrics, the framework also unveils the important roles of longitudinal phonon polaritons in optical response.

Accurate Truncations of Chain Mapping Models for Open Quantum Systems

The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.

Three-Dimensional Au/Ag Nanoparticle/Crossed Carbon Nanotube SERS Substrate for the Detection of Mixed Toxic Molecules

Research on engineering "hotspots" in the field of surface-enhanced Raman scattering (SERS) is at the forefront of contributing to the best sensing indicators. Currently, there is still an urgent need to design a high-strength and large-scale electric field distribution method in order to obtain an ideal SERS sensor. Here, we designed a three-dimensional (3D) Au/Ag nanoparticle (NP)/crossed carbon nanotube film SERS substrate. The proposed structure formed by the simple preparation process can perfectly coordinate the interaction between the SERS substrates, lasers, and molecules. The denser "hotspots" can be induced and then distributed in holes enclosed by Au/AgNPs and the gaps between them. This process was verified by numerical simulations. The experimental results show that the proposed SERS substrate possesses an excellent sensitivity of 10^-12 M (rhodamine 6G (R6G)), an enhancement factor of 1.60 × 10⁹, and a good signal reproducibility (the relative standard deviation is ~6.03%). We further use a Au/AgNP/crossed CNT substrate to detect complex solutions composed of toxic molecules, which shows that our proposed SERS substrate has a wide range of application potentials, especially in food safety.

Fermi's Golden Rule for Spontaneous Emission in Absorptive and Amplifying Media

We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net positive. We show rigorous numerical results of the temporal dynamics of the TLS for an example of two coupled microdisk resonators, forming a gain-loss medium, and demonstrate the clear failure of the commonly adopted formulas based solely on the local density of states.

Bright Optical Eigenmode of 1 nm^{3} Mode Volume

We report on the discovery and rationale to devise bright single optical eigenmodes that feature quantum-optical mode volumes of about 1  nm^{3}. Our findings rely on the development and application of a quasinormal mode theory that self-consistently treats fields and electron nonlocality, spill-out, and Landau damping around atomistic protrusions on a metallic nanoantenna. By outpacing Landau damping with radiation via properly designed antenna modes, the extremely localized modes become bright with radiation efficiencies reaching 30% and could provide up to 4×10^{7} times intensity enhancement.

Light-matter interaction of a molecule in a dissipative cavity from first principles

Cavity-mediated light-matter coupling can dramatically alter opto-electronic and physico-chemical properties of a molecule. Ab initio theoretical predictions of these systems need to combine non-perturbative, many-body electronic structure theory-based methods with cavity quantum electrodynamics and theories of open-quantum systems. Here, we generalize quantum-electrodynamical density functional theory to account for dissipative dynamics of the cavity and describe coupled cavity-single molecule interactions in the weak-to-strong-coupling regimes. Specifically, to establish this generalized technique, we study excited-state dynamics and spectral responses of benzene and toluene under weak-to-strong light-matter coupling. By tuning the coupling, we achieve cavity-mediated energy transfer between electronically excited states. This generalized ab initio quantum-electrodynamical density functional theory treatment can be naturally extended to describe cavity-mediated interactions in arbitrary electromagnetic environments, accessing correlated light-matter observables and thereby closing the gap between electronic structure theory, quantum optics, and nanophotonics.

Few-Mode Field Quantization of Arbitrary Electromagnetic Spectral Densities

We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment. The field quantization requires only the fitting of the spectral density, obtained through classical electromagnetic simulations, to a model system involving a small number of lossy and interacting modes. We illustrate the power and validity of our approach by describing the population and electric field spatial dynamics in the spontaneous decay of an emitter placed in a complex hybrid plasmonic-photonic structure.

On the pole expansion of electromagnetic fields

In several publications, it has been shown how to calculate the near- or far-field properties for a given source or incident field using the resonant states, also known as quasi-normal modes. As previously noted, this pole expansion is not unique, and there exist many equivalent formulations with dispersive expansion coefficients. Here, we approach the pole expansion of the electromagnetic fields using the Mittag-Leffler theorem and obtain another set of formulations with constant weight factors for each pole. We compare the performance and applicability of these formulations using analytical and numerical examples. It turns out that the accuracy of all approaches is rather comparable with a slightly better global convergence of the approach based on a formulation with dispersive expansion coefficients. However, other expansions can be superior locally and are typically faster. Our work will help with selecting appropriate formulations for an efficient description of the electromagnetic response in terms of the resonant states.

Effect of many modes on self-polarization and photochemical suppression in cavities

The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality, the quantum cavity supports a range of photon modes. Here, we demonstrate that as more photon modes are accounted for, physicochemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photon-modes, we find that self-polarization effects become essential, and we introduce the concept of self-polarization-modified Born-Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavity-free Born-Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures, and solids embedded in cavities.

On the applicability of quantum-optical concepts in strong-coupling nanophotonics

Rooted in quantum optics and benefiting from its well-established foundations, strong coupling in nanophotonics has experienced increasing popularity in recent years. With nanophotonics being an experiment-driven field, the absence of appropriate theoretical methods to describe ground-breaking advances has often emerged as an important issue. To address this problem, the temptation to directly transfer and extend concepts already available from quantum optics is strong, even if a rigorous justification is not always available. In this review we discuss situations where, in our view, this strategy has indeed overstepped its bounds. We focus on exciton-plasmon interactions, and particularly on the idea of calculating the number of excitons involved in the coupling. We analyse how, starting from an unfounded interpretation of the term N/V that appears in theoretical descriptions at different levels of complexity, one might be tempted to make independent assumptions for what the number N and the volume V are, and attempt to calculate them separately. Such an approach can lead to different, often contradictory results, depending on the initial assumptions (e.g. through different treatments of V as the-ambiguous in plasmonics-mode volume). We argue that the source of such contradictions is the question itself-How many excitons are coupled?, which disregards the true nature of the coupled components of the system, has no meaning and often not even any practical importance. If one is interested in validating the quantum nature of the system-which appears to be the motivation driving the pursuit of strong coupling with small N-one could instead focus on quantities such as the photon emission rate or the second-order correlation function. While many of the issues discussed here may appear straightforward to specialists, our target audience is predominantly newcomers to the field, either students or scientists specialised in different disciplines. We have thus tried to minimise the occurrence of proofs and overly-technical details, and instead provide a qualitative discussion of analyses that should be avoided, hoping to facilitate further growth of this promising area.

Electromagnetic field quantization and quantum optical input-output relation for grating

A quantization scheme is developed for the radiation and higher order electromagnetic fields in one dimensional periodic, dispersive and absorbing dielectric medium. For this structure, the Green function is solved based on the plane wave expansion method, thus the photon operators, commutation relations and quantum Langevin equations are given and studied based on the Green function approach, moreover, the input-output relations are also derived. It is proved that this quantum theory can be reduced back to that of the predecessors’ study on the homogenous dielectric. Based on this method, we find that the transformation of the photon state through the lossy grating is non-unitary and that the notable non-unitary transformation can be obtained by tuning the imaginary part of the permittivity, we also discussed the excellent quantum optical properties for the grating which are similar to the classical optical phenomena. We believe our work is very beneficial for the control and regulation of the quantum light based on gratings.

Modelling the ultra-strongly coupled spin-boson model with unphysical modes

A quantum system weakly coupled to a zero-temperature environment will relax, via spontaneous emission, to its ground-state. However, when the coupling to the environment is ultra-strong the ground-state is expected to become dressed with virtual excitations. This regime is difficult to capture with some traditional methods because of the explosion in the number of Matsubara frequencies, i.e., exponential terms in the free-bath correlation function. To access this regime we generalize both the hierarchical equations of motion and pseudomode methods, taking into account this explosion using only a biexponential fitting function. We compare these methods to the reaction coordinate mapping, which helps show how these sometimes neglected Matsubara terms are important to regulate detailed balance and prevent the unphysical emission of virtual excitations. For the pseudomode method, we present a general proof of validity for the use of superficially unphysical Matsubara-modes, which mirror the mathematical essence of the Matsubara frequencies.