Quantum Plasmonics in Sub-Atom-Thick Optical Slots.

We show using time-dependent density functional theory (TDDFT) that light can be confined into slot waveguide modes residing between individual atomic layers of coinage metals, such as gold. As the top atomic monolayer lifts a few Å off the underlying bulk Au (111), ab initio electronic structure calculations show that for gaps >1.5 Å, visible light squeezes inside the empty slot underneath, giving optical field distributions 2 Å thick, less than the atomic diameter. Paradoxically classical electromagnetic models are also able to reproduce the resulting dispersion for these subatomic slot modes, where light reaches in-plane wavevectors ∼2 nm-1 and slows to <10-2c. We explain the success of these classical dispersion models for gaps ≥1.5 Å due to a quantum-well state forming in the lifted monolayer in the vicinity of the Fermi level. This extreme trapping of light may explain transient "flare" emission from plasmonic cavities where Raman scattering of metal electrons is greatly enhanced when subatomic slot confinement occurs. Such atomic restructuring of Au under illumination is relevant to many fields, from photocatalysis and molecular electronics to plasmonics and quantum optics.

Molecular Optomechanics Approach to Surface-Enhanced Raman Scattering.

ConspectusMolecular vibrations constitute one of the smallest mechanical oscillators available for micro-/nanoengineering. The energy and strength of molecular oscillations depend delicately on the attached specific functional groups as well as on the chemical and physical environments. By exploiting the inelastic interaction of molecules with optical photons, Raman scattering can access the information contained in molecular vibrations. However, the low efficiency of the Raman process typically allows only for characterizing large numbers of molecules. To circumvent this limitation, plasmonic resonances supported by metallic nanostructures and nanocavities can be used because they localize and enhance light at optical frequencies, enabling surface-enhanced Raman scattering (SERS), where the Raman signal is increased by many orders of magnitude. This enhancement enables few- or even single-molecule characterization. The coupling between a single molecular vibration and a plasmonic mode constitutes an example of an optomechanical interaction, analogous to that existing between cavity photons and mechanical vibrations. Optomechanical systems have been intensely studied because of their fundamental interest as well as their application in practical implementations of quantum technology and sensing. In this context, SERS brings cavity optomechanics down to the molecular scale and gives access to larger vibrational frequencies associated with molecular motion, offering new possibilities for novel optomechanical nanodevices.The molecular optomechanics description of SERS is recent, and its implications have only started to be explored. In this Account, we describe the current understanding and progress of this new description of SERS, focusing on our own contributions to the field. We first show that the quantum description of molecular optomechanics is fully consistent with standard classical and semiclassical models often used to describe SERS. Furthermore, we note that the molecular optomechanics framework naturally accounts for a rich variety of nonlinear effects in the SERS signal with increasing laser intensity.Furthermore, the molecular optomechanics framework provides a tool particularly suited to addressing novel effects of fundamental and practical interest in SERS, such as the emergence of collective phenomena involving many molecules or the modification of the effective losses and energy of the molecular vibrations due to the plasmon-vibration interaction. As compared to standard optomechanics, the plasmonic resonance often differs from a single Lorentzian mode and thus requires a more detailed description of its optical response. This quantum description of SERS also allows us to address the statistics of the Raman photons emitted, enabling the interpretation of two-color correlations of the emerging photons, with potential use in the generation of nonclassical states of light. Current SERS experimental implementations in organic molecules and two-dimensional layers suggest the interest in further exploring intense pulsed illumination, situations of strong coupling, resonant-SERS, and atomic-scale field confinement.

Fano asymmetry in zero-detuned exciton-plasmon systems.

Plasmonic resonances in metallic nanostructures can strongly enhance the emission from quantum emitters, as commonly used in surface-enhanced spectroscopy techniques. The extinction and scattering spectrum of these quantum emitter-metallic nanoantenna hybrid systems are often characterized by a sharp Fano resonance, which is usually expected to be symmetric when a plasmonic mode is resonant with an exciton of the quantum emitter. Here, motivated by recent experimental work showing an asymmetric Fano lineshape under resonant conditions, we study the Fano resonance found in a system composed of a single quantum emitter interacting resonantly with a single spherical silver nanoantenna or with a dimer nanoantenna composed of two gold spherical nanoparticles. To analyze in detail the origin of the resulting Fano asymmetry we develop numerical simulations, an analytical expression that relates the asymmetry of the Fano lineshape to the field enhancement and to the enhanced losses of the quantum emitter (Purcell effect), and a set of simple models. In this manner we identify the contributions to the asymmetry of different physical phenomena, such as retardation and the direct excitation and emission from the quantum emitter.

Quantum surface effects in the electromagnetic coupling between a quantum emitter and a plasmonic nanoantenna: time-dependent density functional theory vs. semiclassical Feibelman approach.

We use time-dependent density functional theory (TDDFT) within the jellium model to study the impact of quantum-mechanical effects on the self-interaction Green's function that governs the electromagnetic interaction between quantum emitters and plasmonic metallic nanoantennas. A semiclassical model based on the Feibelman parameters, which incorporates quantum surface-response corrections into an otherwise classical description, confirms surface-enabled Landau damping and the spill out of the induced charges as the dominant quantum mechanisms strongly affecting the nanoantenna-emitter interaction. These quantum effects produce a redshift and broadening of plasmonic resonances not present in classical theories that consider a local dielectric response of the metals. We show that the Feibelman approach correctly reproduces the nonlocal surface response obtained by full quantum TDDFT calculations for most nanoantenna-emitter configurations. However, when the emitter is located in very close proximity to the nanoantenna surface, we show that the standard Feibelman approach fails, requiring an implementation that explicitly accounts for the nonlocality of the surface response in the direction parallel to the surface. Our study thus provides a fundamental description of the electromagnetic coupling between plasmonic nanoantennas and quantum emitters at the nanoscale.

Electronic Exciton-Plasmon Coupling in a Nanocavity Beyond the Electromagnetic Interaction Picture.

The optical response of a system formed by a quantum emitter and a plasmonic gap nanoantenna is theoretically addressed within the frameworks of classical electrodynamics and the time-dependent density functional theory (TDDFT). A fully quantum many-body description of the electron dynamics within TDDFT allows for analyzing the effect of electronic coupling between the emitter and the nanoantenna, usually ignored in classical descriptions of the optical response. We show that the hybridization between the electronic states of the quantum emitter and those of the metallic nanoparticles strongly modifies the energy, the width, and the very existence of the optical resonances of the coupled system. We thus conclude that the application of a quantum many-body treatment that correctly addresses charge-transfer processes between the emitter and the nanoantenna is crucial to address complex electronic processes involving plasmon-exciton interactions directly impacting optoelectronic applications.

Coupling of Molecular Emitters and Plasmonic Cavities beyond the Point-Dipole Approximation.

As the size of a molecular emitter becomes comparable to the dimensions of a nearby optical resonator, the standard approach that considers the emitter to be a point-like dipole breaks down. By adoption of a quantum description of the electronic transitions of organic molecular emitters, coupled to a plasmonic electromagnetic field, we are able to accurately calculate the position-dependent coupling strength between a plasmon and an emitter. The spatial distribution of excitonic and photonic quantum states is found to be a key aspect in determining the dynamics of molecular emission in ultrasmall cavities both in the weak and strong coupling regimes. Moreover, we show that the extreme localization of plasmonic fields leads to the selection rule breaking of molecular excitations.

Revealing the quantum regime in tunnelling plasmonics.

When two metal nanostructures are placed nanometres apart, their optically driven free electrons couple electrically across the gap. The resulting plasmons have enhanced optical fields of a specific colour tightly confined inside the gap. Many emerging nanophotonic technologies depend on the careful control of this plasmonic coupling, including optical nanoantennas for high-sensitivity chemical and biological sensors, nanoscale control of active devices, and improved photovoltaic devices. But for subnanometre gaps, coherent quantum tunnelling becomes possible and the system enters a regime of extreme non-locality in which previous classical treatments fail. Electron correlations across the gap that are driven by quantum tunnelling require a new description of non-local transport, which is crucial in nanoscale optoelectronics and single-molecule electronics. Here, by simultaneously measuring both the electrical and optical properties of two gold nanostructures with controllable subnanometre separation, we reveal the quantum regime of tunnelling plasmonics in unprecedented detail. All observed phenomena are in good agreement with recent quantum-based models of plasmonic systems, which eliminate the singularities predicted by classical theories. These findings imply that tunnelling establishes a quantum limit for plasmonic field confinement of about 10(-8)λ(3) for visible light (of wavelength λ). Our work thus prompts new theoretical and experimental investigations into quantum-domain plasmonic systems, and will affect the future of nanoplasmonic device engineering and nanoscale photochemistry.

Self-assembled flat-faceted nanoparticles chains as a highly-tunable platform for plasmon-enhanced spectroscopy in the infrared.

Self-assembly fabrication methods can produce aggregates of metallic nanoparticles separated by nanometer distances which act as versatile platforms for field-enhanced spectroscopy due to the strong fields induced at the interparticle gaps. In this letter we show the advantages of using particles with large flat facets at the gap as the building elements of the aggregates. For this purpose, we analyze theoretically the plasmonic response of chains of metallic particles of increasing length. These chains may be a direct product of the chemical synthesis and can be seen as the key structural unit behind the plasmonic response of two and three dimensional self-assembled aggregates. The longitudinal chain plasmon that dominates the optical response redshifts following an exponential dependence on the number of particles in the chain for all facets studied, with a saturation wavelength and a characteristic decay length depending linearly on the diameter of the facet. According to our calculations, for small Au particles of 50 nm size separated by a 1 nanometer gap, the saturation wavelength for the largest facets considered correspond to a wavelength shift of ≈ 1200 nm with respect to the single particle resonance, compared to shifts of only ≈ 200 nm for the equivalent configuration of perfectly spherical particles. The corresponding decay lengths are 11.8 particles for the faceted nanoparticles and 3.5 particles for the spherical ones. Thus, large flat facets lead to an excellent tunability of the longitudinal chain plasmon, covering the whole biological window and beyond. Furthermore, the maximum near-field at the gap is only moderately weaker for faceted gaps than for spherical particles, while the region of strong local field enhancement extends over a considerably larger volume, allowing to accommodate more target molecules. Our results indicate that flat facets introduce significant advantages for spectroscopic and sensing applications using self-assembled aggregates.

Linking classical and molecular optomechanics descriptions of SERS.

The surface-enhanced Raman scattering (SERS) of molecular species in plasmonic cavities can be described as an optomechanical process where plasmons constitute an optical cavity of reduced effective mode volume which effectively couples to the vibrations of the molecules. An optomechanical Hamiltonian can address the full quantum dynamics of the system, including the phonon population build-up, the vibrational pumping regime, and the Stokes-anti-Stokes correlations of the photons emitted. Here we describe in detail two different levels of approximation to the methodological solution of the optomechanical Hamiltonian of a generic SERS configuration, and compare the results of each model in light of recent experiments. Furthermore, a phenomenological semi-classical approach based on a rate equation of the phonon population is demonstrated to be formally equivalent to that obtained from the full quantum optomechanical approach. The evolution of the Raman signal with laser intensity (thermal, vibrational pumping and instability regimes) is accurately addressed when this phenomenological semi-classical approach is properly extended to account for the anti-Stokes process. The formal equivalence between semi-classical and molecular optomechanics descriptions allows us to describe the vibrational pumping regime of SERS through the classical cross sections which characterize a nanosystem, thus setting a roadmap to describing molecular optomechanical effects in a variety of experimental situations.

Monitoring Early-Stage Nanoparticle Assembly in Microdroplets by Optical Spectroscopy and SERS.

Microfluidic microdroplets have increasingly found application in biomolecular sensing as well as nanomaterials growth. More recently the synthesis of plasmonic nanostructures in microdroplets has led to surface-enhanced Raman spectroscopy (SERS)-based sensing applications. However, the study of nanoassembly in microdroplets has previously been hindered by the lack of on-chip characterization tools, particularly at early timescales. Enabled by a refractive index matching microdroplet formulation, dark-field spectroscopy is exploited to directly track the formation of nanometer-spaced gold nanoparticle assemblies in microdroplets. Measurements in flow provide millisecond time resolution through the assembly process, allowing identification of a regime where dimer formation dominates the dark-field scattering and SERS. Furthermore, it is shown that small numbers of nanoparticles can be isolated in microdroplets, paving the way for simple high-yield assembly, isolation, and sorting of few nanoparticle structures.

Gold nanorods with sub-nanometer separation using cucurbit[n]uril for SERS applications.

The capability of cucurbit[n]uril to align gold nanorods, leading to optical coupling into the infrared region, is shown. Cryo-TEM and tomographic imaging confirm the presence of aligned Au nanorods. Full electromagnetic simulations, which support the observed plasmonic modes and predict large enhancements in the inter-particle junction, are performed. This construct is then further utilized for surface enhanced Raman spectroscopy.

Uncovering low-frequency vibrations in surface-enhanced Raman of organic molecules.

Accessing the terahertz (THz) spectral domain through surface-enhanced Raman spectroscopy (SERS) is challenging and opens up the study of low-frequency molecular and electronic excitations. Compared to direct THz probing of heterogenous ensembles, the extreme plasmonic confinement of visible light to deep sub-wavelength scales allows the study of hundreds or even single molecules. We show that self-assembled molecular monolayers of a set of simple aromatic thiols confined inside single-particle plasmonic nanocavities can be distinguished by their low-wavenumber spectral peaks below 200 cm-1, after removal of a bosonic inelastic contribution and an exponential background from the spectrum. Developing environment-dependent density-functional-theory simulations of the metal-molecule configuration enables the assignment and classification of their THz vibrations as well as the identification of intermolecular coupling effects and of the influence of the gold surface configuration. Furthermore, we show dramatically narrower THz SERS spectra from individual molecules at picocavities, which indicates the possibility to study intrinsic vibrational properties beyond inhomogeneous broadening, further supporting the key role of local environment.

Giant Quantum Electrodynamic Effects on Single SiV Color Centers in Nanosized Diamonds.

Understanding and mastering quantum electrodynamics phenomena is essential to the development of quantum nanophotonics applications. While tailoring of the local vacuum field has been widely used to tune the luminescence rate and directionality of a quantum emitter, its impact on their transition energies is barely investigated and exploited. Fluorescent defects in nanosized diamonds constitute an attractive nanophotonic platform to investigate the Lamb shift of an emitter embedded in a dielectric nanostructure with high refractive index. Using spectral and time-resolved optical spectroscopy of single SiV defects, we unveil blue shifts (up to 80 meV) of their emission lines, which are interpreted from model calculations as giant Lamb shifts. Moreover, evidence for a positive correlation between their fluorescence decay rates and emission line widths is observed, as a signature of modifications not only of the photonic local density of states but also of the phononic one, as the nanodiamond size is decreased. Correlative light-electron microscopy of single SiVs and their host nanodiamonds further supports these findings. These results make nanodiamond-SiVs promising as optically driven spin qubits and quantum light sources tunable through nanoscale tailoring of vacuum-field fluctuations.

Giant optomechanical spring effect in plasmonic nano- and picocavities probed by surface-enhanced Raman scattering.

Molecular vibrations couple to visible light only weakly, have small mutual interactions, and hence are often ignored for non-linear optics. Here we show the extreme confinement provided by plasmonic nano- and pico-cavities can sufficiently enhance optomechanical coupling so that intense laser illumination drastically softens the molecular bonds. This optomechanical pumping regime produces strong distortions of the Raman vibrational spectrum related to giant vibrational frequency shifts from an optical spring effect which is hundred-fold larger than in traditional cavities. The theoretical simulations accounting for the multimodal nanocavity response and near-field-induced collective phonon interactions are consistent with the experimentally-observed non-linear behavior exhibited in the Raman spectra of nanoparticle-on-mirror constructs illuminated by ultrafast laser pulses. Further, we show indications that plasmonic picocavities allow us to access the optical spring effect in single molecules with continuous illumination. Driving the collective phonon in the nanocavity paves the way to control reversible bond softening, as well as irreversible chemistry.

How chain plasmons govern the optical response in strongly interacting self-assembled metallic clusters of nanoparticles.

Self-assembled clusters of metallic nanoparticles separated by nanometric gaps generate strong plasmonic modes that support both intense and localized near fields. These find use in many ultrasensitive chemical and biological sensing applications through surface enhanced Raman scattering (SERS). The inability to control at the nanoscale the structure of the clusters on which the optical response crucially depends, has led to the development of general descriptions to model the various morphologies fabricated. Here, we use rigorous electrodynamic calculations to study clusters formed by a hundred nanospheres that are separated by ∼1 nm distance, set by the dimensions of the macrocyclic molecular linker employed experimentally. Three-dimensional (3D) cluster structures of moderate compactness are of special interest since they resemble self-assembled clusters grown under typical diffusion-limited aggregation conditions. We find very good agreement between the simulated and measured far-field extinction spectra, supporting the equivalence of the assumed and experimental morphologies. From these results we argue that the main features of the optical response of two- and three-dimensional clusters can be understood in terms of the excitation of simple units composed of different length resonant chains. Notably, we observe a qualitative difference between short- and long-chain modes in both spectral response and spatial distribution: dimer and short-chain modes are observed in the periphery of the cluster at higher energies, whereas inside the structure longer chain excitation occurs at lower energies. We study in detail different configurations of isolated one-dimensional chains as prototypical building blocks for large clusters, showing that the optical response of the chains is robust to disorder. This study provides an intuitive understanding of the behavior of very complex aggregates and may be generalized to other types of aggregates and systems formed by large numbers of strongly interacting particles.

Remote near-field spectroscopy of vibrational strong coupling between organic molecules and phononic nanoresonators.

Phonon polariton (PhP) nanoresonators can dramatically enhance the coupling of molecular vibrations and infrared light, enabling ultrasensitive spectroscopies and strong coupling with minute amounts of matter. So far, this coupling and the resulting localized hybrid polariton modes have been studied only by far-field spectroscopy, preventing access to modal near-field patterns and dark modes, which could further our fundamental understanding of nanoscale vibrational strong coupling (VSC). Here we use infrared near-field spectroscopy to study the coupling between the localized modes of PhP nanoresonators made of h-BN and molecular vibrations. For a most direct probing of the resonator-molecule coupling, we avoid the direct near-field interaction between tip and molecules by probing the molecule-free part of partially molecule-covered nanoresonators, which we refer to as remote near-field probing. We obtain spatially and spectrally resolved maps of the hybrid polariton modes, as well as the corresponding coupling strengths, demonstrating VSC on a single PhP nanoresonator level. Our work paves the way for near-field spectroscopy of VSC phenomena not accessible by conventional techniques.

Complex plasmon-exciton dynamics revealed through quantum dot light emission in a nanocavity.

Plasmonic cavities can confine electromagnetic radiation to deep sub-wavelength regimes. This facilitates strong coupling phenomena to be observed at the limit of individual quantum emitters. Here, we report an extensive set of measurements of plasmonic cavities hosting one to a few semiconductor quantum dots. Scattering spectra show Rabi splitting, demonstrating that these devices are close to the strong coupling regime. Using Hanbury Brown and Twiss interferometry, we observe non-classical emission, allowing us to directly determine the number of emitters in each device. Surprising features in photoluminescence spectra point to the contribution of multiple excited states. Using model simulations based on an extended Jaynes-Cummings Hamiltonian, we find that the involvement of a dark state of the quantum dots explains the experimental findings. The coupling of quantum emitters to plasmonic cavities thus exposes complex relaxation pathways and emerges as an unconventional means to control dynamics of quantum states.

Microcavity phonon polaritons from the weak to the ultrastrong phonon-photon coupling regime.

Strong coupling between molecular vibrations and microcavity modes has been demonstrated to modify physical and chemical properties of the molecular material. Here, we study the less explored coupling between lattice vibrations (phonons) and microcavity modes. Embedding thin layers of hexagonal boron nitride (hBN) into classical microcavities, we demonstrate the evolution from weak to ultrastrong phonon-photon coupling when the hBN thickness is increased from a few nanometers to a fully filled cavity. Remarkably, strong coupling is achieved for hBN layers as thin as 10 nm. Further, the ultrastrong coupling in fully filled cavities yields a polariton dispersion matching that of phonon polaritons in bulk hBN, highlighting that the maximum light-matter coupling in microcavities is limited to the coupling strength between photons and the bulk material. Tunable cavity phonon polaritons could become a versatile platform for studying how the coupling strength between photons and phonons may modify the properties of polar crystals.

Addressing molecular optomechanical effects in nanocavity-enhanced Raman scattering beyond the single plasmonic mode.

The description of surface-enhanced Raman scattering (SERS) as a molecular optomechanical process has provided new insights into the vibrational dynamics and nonlinearities of this inelastic scattering process. In earlier studies, molecular vibrations have typically been assumed to couple with a single plasmonic mode of a metallic nanostructure, ignoring the complexity of the plasmonic response in many configurations of practical interest such as in metallic nanojunctions. By describing the plasmonic fields as a continuum, we demonstrate here the importance of considering the full plasmonic response to properly address the molecule-cavity optomechanical interaction. We apply the continuum-field model to calculate the Raman signal from a single molecule in a plasmonic nanocavity formed by a nanoparticle-on-a-mirror configuration, and compare the results of optomechanical parameters, vibrational populations, and Stokes and anti-Stokes signals of the continuum-field model with those obtained from the single-mode model. Our results reveal that high-order non-radiative plasmonic modes significantly modify the optomechanical behavior under strong laser illumination. Moreover, Raman linewidths, lineshifts, vibrational populations, and parametric instabilities are found to be sensitive to the energy of the molecular vibrational modes. The implications of adopting the continuum-field model to describe the plasmonic cavity response in molecular optomechanics are relevant in many other nanoantenna and nanocavity configurations commonly used to enhance SERS.

Boron nitride nanoresonators for phonon-enhanced molecular vibrational spectroscopy at the strong coupling limit.

Enhanced light-matter interactions are the basis of surface-enhanced infrared absorption (SEIRA) spectroscopy, and conventionally rely on plasmonic materials and their capability to focus light to nanoscale spot sizes. Phonon polariton nanoresonators made of polar crystals could represent an interesting alternative, since they exhibit large quality factors, which go far beyond those of their plasmonic counterparts. The recent emergence of van der Waals crystals enables the fabrication of high-quality nanophotonic resonators based on phonon polaritons, as reported for the prototypical infrared-phononic material hexagonal boron nitride (h-BN). In this work we use, for the first time, phonon-polariton-resonant h-BN ribbons for SEIRA spectroscopy of small amounts of organic molecules in Fourier transform infrared spectroscopy. Strikingly, the interaction between phonon polaritons and molecular vibrations reaches experimentally the onset of the strong coupling regime, while numerical simulations predict that vibrational strong coupling can be fully achieved. Phonon polariton nanoresonators thus could become a viable platform for sensing, local control of chemical reactivity and infrared quantum cavity optics experiments.