Strong coupling in plasmonic metal nanoparticles

The study of strong coupling between light and matter has gained significant attention in recent years due to its potential applications in diverse fields, including artificial light harvesting, ultraefficient polariton lasing, and quantum information processing. Plasmonic cavities are a compelling alternative of conventional photonic resonators, enabling ultracompact polaritonic systems to operate at room temperature. This review focuses on colloidal metal nanoparticles, highlighting their advantages as plasmonic cavities in terms of their facile synthesis, tunable plasmonic properties, and easy integration with excitonic materials. We explore recent examples of strong coupling in single nanoparticles, dimers, nanoparticle-on-a-mirror configurations, and other types of nanoparticle-based resonators. These systems are coupled with an array of excitonic materials, including atomic emitters, semiconductor quantum dots, two-dimensional materials, and perovskites. In the concluding section, we offer perspectives on the future of strong coupling research in nanoparticle systems, emphasizing the challenges and potentials that lie ahead. By offering a thorough understanding of the current state of research in this field, we aim to inspire further investigations and advances in the study of strongly coupled nanoparticle systems, ultimately unlocking new avenues in nanophotonic applications.

Highly Localized Surface Plasmon Nanolasers via Strong Coupling

Surface plasmons have robust and strong confinement to the light field which is beneficial for the light-matter interaction. Surface plasmon amplification by stimulated emission of radiation (SPACER) has the potential to be integrated on the semiconductor chip as a compact coherent light source, which can play an important role in further extension of Moore's law. In this study, we demonstrate the localized surface plasmon lasing at room temperature in the communication band using metallic nanoholes as the plasmonic nanocavity and InP nanowires as the gain medium. Optimizing laser performance has been demonstrated by coupling between two metallic nanoholes which adds another degree of freedom for manipulating the lasing properties. Our plasmonic nanolasers exhibit lower power consumption, smaller mode volumes, and higher spontaneous emission coupling factors due to enhanced light-matter interactions, which are very promising in the applications of high-density sensing and photonic integrated circuits.

Entanglement generation by strong coupling between surface lattice resonance and exciton in an Al nanoarray-coated WS2 quantum emitter

Strong light-matter interaction plays a central role in realizing quantum photonic technologies. The entanglement state, which results from the hybridization of excitons and cavity photons, forms the foundation of quantum information science. In this work, an entanglement state is achieved by manipulating the mode coupling between surface lattice resonance and quantum emitter into the strong coupling regime. At the same time, a Rabi splitting of 40 meV is observed. A full quantum model based on the Heisenberg picture is used to describe this unclassical phenomenon, and it perfectly explains the interaction and dissipation process. In addition, the observed concurrency degree of the entanglement state is 0.5, presenting the quantum nonlocality. This work effectively contributes to the understanding of nonclassical quantum effects arising from strong coupling and will intrigue more interesting potential applications in quantum optics.

Ultra-confined Propagating Exciton-Plasmon Polaritons Enabled by Cavity-Free Strong Coupling: Beating Plasmonic Trade-Offs

Hybrid coupling systems consisting of transition metal dichalcogenides (TMD) and plasmonic nanostructures have emerged as a promising platform to explore exciton-plasmon polaritons. However, the requisite cavity/resonator for strong coupling introduces extra complexities and challenges for waveguiding applications. Alternatively, plasmonic nano-waveguides can also be utilized to provide a non-resonant approach for strong coupling, while their utility is limited by the plasmonic confinement-loss and confinement-momentum trade-offs. Here, based on a cavity-free approach, we overcome these constraints by theoretically strong coupling of a monolayer TMD to a single metal nanowire, generating ultra-confined propagating exciton-plasmon polaritons (PEPPs) that beat the plasmonic trade-offs. By leveraging strong-coupling-induced reformations in energy distribution and combining favorable properties of surface plasmon polaritons (SPPs) and excitons, the generated PEPPs feature ultra-deep subwavelength confinement (down to 1-nm level with mode areas ~ 10^-4 of λ²), long propagation length (up to ~ 60 µm), tunable dispersion with versatile mode characters (SPP- and exciton-like mode characters), and small momentum mismatch to free-space photons. With the capability to overcome the trade-offs of SPPs and the compatibility for waveguiding applications, our theoretical results suggest an attractive guided-wave platform to manipulate exciton-plasmon interactions at the ultra-deep subwavelength scale, opening new horizons for waveguiding nano-polaritonic components and devices.

Correlated spectrum of distant semiconductor qubits coupled by microwave photons

We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons. These patterns are in excellent agreement with a simulation using the Tavis-Cummings model, and allow us to readily identify different parameter regimes for both qubits in the detuning space. This method could potentially be an important component in the overall spectroscopic toolbox for quickly characterizing certain collective properties of multiple cavity quantum electrodynamics (QED) coupled qubits.

Engineering the Spectral and Spatial Dispersion of Thermal Emission via Polariton-Phonon Strong Coupling

Strong coupling between optical modes can be implemented into nanophotonic design to modify the energy-momentum dispersion relation. This approach offers potential avenues for tuning the thermal emission frequency, line width, polarization, and spatial coherence. Here, we employ three-mode strong coupling between propagating and localized surface phonon polaritons, with zone-folded longitudinal optic phonons within periodic arrays of 4H-SiC nanopillars. Energy exchange, mode evolution, and coupling strength between the three polariton branches are explored experimentally and theoretically. The influence of strong coupling upon the angle-dependent thermal emission was directly measured, providing excellent agreement with theory. We demonstrate a 5-fold improvement in the spatial coherence and 3-fold enhancement of the quality factor of the polaritonic modes, with these hybrid modes also exhibiting a mixed character that could enable opportunities to realize electrically driven emission. Our results show that polariton-phonon strong coupling enables thermal emitters, which meet the requirements for a host of IR applications in a simple, lightweight, narrow-band, and yet bright emitter.

Enhancing Vibrational Light-Matter Coupling Strength beyond the Molecular Concentration Limit Using Plasmonic Arrays

Vibrational strong coupling is emerging as a promising tool to modify molecular properties by making use of hybrid light-matter states known as polaritons. Fabry-Perot cavities filled with organic molecules are typically used, and the molecular concentration limits the maximum reachable coupling strength. Developing methods to increase the coupling strength beyond the molecular concentration limit are highly desirable. In this Letter, we investigate the effect of adding a gold nanorod array into a cavity containing pure organic molecules using FT-IR microscopy and numerical modeling. Incorporation of the plasmonic nanorod array that acts as artificial molecules leads to an order of magnitude increase in the total coupling strength for the cavity with matching resonant frequency filled with organic molecules. Additionally, we observe a significant narrowing of the plasmon line width inside the cavity. We anticipate that these results will be a step forward in exploring vibropolaritonic chemistry and may be used in plasmon based biosensors.

Phonon-Polaritons in Lead Halide Perovskite Film Hybridized with THz Metamaterials

In this work, we demonstrated a phonon-polariton in the terahertz (THz) frequency range, generated in a crystallized lead halide perovskite film coated on metamaterials. When the metamaterial resonance was in tune with the phonon resonance of the perovskite film, Rabi splitting occurred due to the strong coupling between the resonances. The Rabi splitting energy was about 1.1 meV, which is larger than the metamaterial and phonon resonance line widths; the interaction potential estimation confirmed that the strong coupling regime was reached successfully. We were able to tune the polaritonic branches by varying the metamaterial resonance, thereby obtaining the dispersion curve with a clear anticrossing behavior. Additionally, we performed in situ THz spectroscopy as we annealed the perovskite film and studied the Rabi splitting as a function of the films' crystallization coverage. The Rabi splitting versus crystallization volume fraction exhibited a unique power-law scaling, depending on the crystal growth dimensions.

Strongly Coupled Exciton-Surface Lattice Resonances Engineer Long-Range Energy Propagation

Achieving propagation lengths in hybrid plasmonic systems beyond typical values of tens of micrometers is important for quantum plasmonics applications. We report long-range optical energy propagation due to excitons in semiconductor quantum dots (SQDs) being strongly coupled to surface lattice resonance (SLRs) in silver nanoparticle arrays. Photoluminescence (PL) measurements provide evidence of an exciton-SLR (ESLR) mode extending at least 600 μm from the excitation region. We also observe additional energy propagation with range well beyond the ESLR mode and with dependency on the coupling strength, g, between SQDs and SLR. Cavity quantum electrodynamics calculations capture the nature of the PL spectra for consistent g values, while coupled dipole calculations show a SQD number-dependent electric field decay profile consistent with the experimental spatial PL profile. Our results suggest an exciting direction wherein SLRs mediate long-range interactions between SQDs, having possible applications in optoelectronics, sensing, and quantum information science.

Visualizing Spatial Variations of Plasmon-Exciton Polaritons at the Nanoscale Using Electron Microscopy

Polaritons are compositional light-matter quasiparticles that have enabled remarkable breakthroughs in quantum and nonlinear optics, as well as in material science. Recently, plasmon-exciton polaritons (plexcitons) have been realized in hybrid material systems composed of transition metal dichalcogenide (TMDC) materials and metal nanoparticles, expanding polaritonic concepts to room temperature and nanoscale systems that also benefit from the exotic properties of TMDC materials. Despite the enormous progress in understanding TMDC-based plexcitons using optical-based methods, experimental evidence of plexcitons formation has remained indirect and mapping their nanometer-scale characteristics has remained an open challenge. Here, we demonstrate that plexcitons generated by a hybrid system composed of an individual silver nanoparticle and a few-layer WS₂ flake can be spectroscopically mapped with nanometer spatial resolution using electron energy loss spectroscopy in a scanning transmission electron microscope. Experimental anticrossing measurements using the absorption-dominated extinction signal provide the ultimate evidence for plexciton hybridization in the strong coupling regime. Spatially resolved EELS maps reveal the existence of unexpected nanoscale variations in the deep-subwavelength nature of plexcitons generated by this system. These findings pioneer new possibilities for in-depth studies of the local atomic structure dependence of polariton-related phenomena in TMDC hybrid material systems with nanometer spatial resolution.

Strong Coupling between a Quasi-single Molecule and a Plasmonic Cavity in the Trapping System

We theoretically investigate the strong coupling phenomenon between a quasi-single molecule and a plasmonic cavity based on the blue-detuned trapping system. The trapping system is made up of a metallic nanohole array. A finite-difference time-domain method is employed to simulate the system, and the molecule is treated as a dipole in simulations. By calculating the electromagnetic field distributions, we obtain the best position for trapping a molecule, and we get the strong coupling phenomenon that there are two splitting peaks in the transmission spectrum when the molecule is trapped in the structure, while only one peak is observed in the one without the molecule. We also find that only when the molecule polarization parallels to the incident light wave vector can we observe a strong coupling phenomenon.

Room-Temperature Strong Coupling of CdSe Nanoplatelets and Plasmonic Hole Arrays

Exciton polaritons are hybrid light-matter quasiparticles that can serve as coherent light sources. Motivated by applications, room-temperature realization of polaritons requires narrow, excitonic transitions with large transition dipoles. Such transitions must then be strongly coupled to an electromagnetic mode confined in a small volume. While much work has explored polaritons in organic materials, semiconductor nanocrystals present an alternative excitonic system with enhanced photostability and spectral tunability. In particular, quasi-two-dimensional nanocrystals known as nanoplatelets (NPLs) exhibit intense, spectrally narrow excitonic transitions useful for polariton formation. Here, we place CdSe NPLs on silver hole arrays to demonstrate exciton-plasmon polaritons at room temperature. Angle-resolved reflection spectra reveal Rabi splittings up to 149 meV for the polariton states. We observe bright, polarized emission arising from the lowest polariton state. Furthermore, we assess the dependence of the Rabi splitting on the hole-array pitch and the number N of NPLs. While the pitch determines the in-plane momentum for which strong coupling is observed, it does not affect the size of the splitting. The Rabi splitting first increases with NPL film thickness before eventually saturating. Instead of the commonly used [Formula: see text] dependence, we develop an analytical expression that includes the transverse confinement of the plasmon modes to describe the measured Rabi splitting as a function of NPL film thickness.

Proton detection of carbon-carbon couplings in symmetrical molecules: Analytical explanation, SYMONA pulse sequence

The approach to the measurement of one-bond indirect spin-spin coupling constants between equivalent nuclei was revisited. The analytical formulas for development of the density matrix of strongly coupled symmetrical HC-C'H' spin systems were derived and the optimal duration of polarization delay in the original 2QHMBC pulse sequence is discussed. Based on the analytical formulas a new version of a robust indirect detection experiment, called SYMONA (SYmmetrical MOlecules Natural Abundance double-quantum experiment), was proposed for carbon-carbon coupling constants detection in symmetrical molecules. Additionally, application of the SYMONA experiment to more complicated spin systems than isolated HC-C'H' is discussed.

Strong Light-Matter Coupling between Plasmons in Individual Gold Bi-pyramids and Excitons in Mono- and Multilayer WSe2

Monolayer transition-metal dichalcogenides (TMDCs) have attracted a lot of research attention recently, motivated by their remarkable optical properties and potential for strong light-matter interactions. Realization of strong plasmon-exciton coupling is especially desirable in this context because it holds promise for the enabling of room-temperature quantum and nonlinear optical applications. These efforts naturally require investigations at a single-nanoantenna level, which, in turn, should possess a compact optical mode interacting with a small amount of excitonic material. However, standard plasmonic nanoantenna designs such as nanoparticle dimers or particle-on-film suffer from misalignment of the local electric field in the gap with the in-plane transition dipole moment of monolayer TMDCs. Here, we circumvent this problem by utilizing gold bi-pyramids (BPs) as very efficient plasmonic nanoantennas. We demonstrate strong coupling between individual BPs and tungsten diselenide (WSe₂) monolayers at room temperature. We further study the coupling between multilayers of WSe₂ and BPs to elucidate the effect of the number of layers on the coupling strength. Importantly, BPs adopt a reduced-symmetry configuration when deposited on WSe₂, such that only one sharp antenna tip efficiently interacts with excitons. Despite the small interaction area, we manage to achieve strong coupling, with Rabi splitting exceeding ∼100 meV. Our results suggest a feasible way toward realizing plasmon-exciton polaritons involving nanoscopic areas of TMDCs, thus pointing toward quantum and nonlinear optics applications at ambient conditions.

A practical strategy for the accurate measurement of residual dipolar couplings in strongly aligned small molecules

Accurate measurement of residual dipolar couplings (RDCs) requires an appropriate degree of alignment in order to optimize data quality. An overly weak alignment yields very small anisotropic data that are susceptible to measurement errors, whereas an overly strong alignment introduces extensive anisotropic effects that severely degrade spectral quality. The ideal alignment amplitude also depends on the specific pulse sequence used for the coupling measurement. In this work, we introduce a practical strategy for the accurate measurement of one-bond ¹³C-¹H RDCs up to a range of ca. -300 to +300 Hz, corresponding to an alignment that is an order of magnitude stronger than typically employed for small molecule structural elucidation. This strong alignment was generated in the mesophase of the commercially available poly-γ-(benzyl-L-glutamate) polymer. The total coupling was measured by the simple and well-studied heteronuclear two-dimensional J-resolved experiment, which performs well in the presence of strong anisotropic effects. In order to unequivocally determine the sign of the total coupling and resolve ambiguities in assigning total couplings in the CH₂ group, coupling measurements were conducted at an isotropic condition plus two anisotropic conditions of different alignment amplitudes. Most RDCs could be readily extracted from these measurements whereas more complicated spectral effects resulting from strong homonuclear coupling could be interpreted either theoretically or by simulation. Importantly, measurement of these very large RDCs actually offers significantly improved data quality and utility for the structure determination of small organic molecules.

Observation of Tunable Charged Exciton Polaritons in Hybrid Monolayer WS2-Plasmonic Nanoantenna System

Formation of dressed light-matter states in optical structures, manifested as Rabi splitting of the eigen energies of a coupled system, is one of the key effects in quantum optics. In pursuing this regime with semiconductors, light is usually made to interact with excitons, electrically neutral quasiparticles of semiconductors; meanwhile interactions with charged three-particle states, trions, have received little attention. Here, we report on strong interaction between localized surface plasmons in silver nanoprisms and excitons and trions in monolayer tungsten disulfide (WS₂). We show that the plasmon-exciton interactions in this system can be efficiently tuned by controlling the charged versus neutral exciton contribution to the coupling process. In particular, we show that a stable trion state emerges and couples efficiently to the plasmon resonance at low temperature by forming three bright intermixed plasmon-exciton-trion polariton states. Our findings open up a possibility to exploit electrically charged polaritons at the single nanoparticle level.

A pure shift experiment with increased sensitivity and superior performance for strongly coupled systems

Motivated by the persisting need for enhanced resolution in solution state NMR spectra, pure shift techniques such as Zangger-Sterk decoupling have recently attracted widespread interest. These techniques for homonuclear decoupling offer enhanced resolution in one- and multidimensional proton detected experiments by simplifying multiplet structures. In this work, a modification to the popular Zangger-Sterk technique PEPSIE (Perfect Echo Pure Shift Improved Experiment) is presented, which decouples pairs of spins even if they share the same volume element. This in turn can drastically improve the sensitivity, as compared to classical Zangger-Sterk decoupling, as larger volume elements can be used to collect the detected signal. Most interestingly, even in the presence of moderate strong coupling, the PEPSIE experiment produces clean and widely artifact free spectra. In order to better understand this - to us initially - surprising behaviour we performed analyses using numerical simulations and derived an (approximate) analytical solution from density matrix formalism. We show that this experiment is particularly suitable to study samples with strong signal clustering, a situation which can render classic Zangger-Sterk decoupling inefficient.

Manipulating Coherent Plasmon-Exciton Interaction in a Single Silver Nanorod on Monolayer WSe2

Strong coupling between plasmons and excitons in nanocavities can result in the formation of hybrid plexcitonic states. Understanding the dispersion relation of plexcitons is important both for fundamental quantum science and for applications including optoelectronics and nonlinear optics devices. The conventional approach, based on statistics over different nanocavities, suffers from large inhomogeneities from the samples, owing to the nonuniformity of nanocavities and the lack of control over the locations and orientations of the excitons. Here we report the first measurement of the dispersion relationship of plexcitons in an individual nanocavity. Using a single silver nanorod as a Fabry-Pérot nanocavity, we realize strong coupling of plasmon in single nanocavity with excitons in a single atomic layer of tungsten diselenide. The plexciton dispersion is measured by in situ redshifting the plasmon energy via successive deposition of a dielectric layer. Room-temperature formation of plexcitons with Rabi splittings as large as 49.5 meV is observed. The realization of strong plasmon-exciton coupling by in situ tuning of the plasmon provides a novel route for the manipulation of excitons in semiconductors.

Mode Modification of Plasmonic Gap Resonances Induced by Strong Coupling with Molecular Excitons

Plasmonic cavities can be used to control the atom-photon coupling process at the nanoscale, since they provide an ultrahigh density of optical states in an exceptionally small mode volume. Here we demonstrate strong coupling between molecular excitons and plasmonic resonances (so-called plexcitonic coupling) in a film-coupled nanocube cavity, which can induce profound and significant spectral and spatial modifications to the plasmonic gap modes. Within the spectral span of a single gap mode in the nanocube-film cavity with a 3 nm wide gap, the introduction of narrow-band J-aggregate dye molecules not only enables an anticrossing behavior in the spectral response but also splits the single spatial mode into two distinct modes that are easily identified by their far-field scattering profiles. Simulation results confirm the experimental findings, and the sensitivity of the plexcitonic coupling is explored using digital control of the gap spacing. Our work opens up a new perspective to study the strong coupling process, greatly extending the functionality of nanophotonic systems, with the potential to be applied in cavity quantum electrodynamic systems.

Observation of Mode Splitting in Photoluminescence of Individual Plasmonic Nanoparticles Strongly Coupled to Molecular Excitons

Plasmon-exciton interactions are important for many prominent spectroscopic applications such as surface-enhanced Raman scattering, plasmon-mediated fluorescence, nanoscale lasing, and strong coupling. The case of strong coupling is analogous to quantum optical effects studied in solid state and atomic systems previously. In plasmonics, similar observations have been almost exclusively made in elastic scattering experiments; however, the interpretation of these experiments is often cumbersome. Here, we demonstrate mode splitting not only in scattering, but also in photoluminescence of individual hybrid nanosystems, which manifests a direct proof of strong coupling in plasmon-exciton nanoparticles. We achieved these results due to saturation of the mode volume with molecular J-aggregates, which resulted in splitting up to 400 meV, that is, ∼20% of the resonance energy. We analyzed the correlation between scattering and photoluminescence and found that splitting in photoluminescence is considerably less than that in scattering. Moreover, we found that splitting in both photoluminescence and scattering signals increased upon cooling to cryogenic temperatures. These findings improve our understanding of strong coupling phenomena in plasmonics.

Strong Coupling of Localized Surface Plasmons to Excitons in Light-Harvesting Complexes

Gold nanostructure arrays exhibit surface plasmon resonances that split after attaching light harvesting complexes 1 and 2 (LH1 and LH2) from purple bacteria. The splitting is attributed to strong coupling between the localized surface plasmon resonances and excitons in the light-harvesting complexes. Wild-type and mutant LH1 and LH2 from Rhodobacter sphaeroides containing different carotenoids yield different splitting energies, demonstrating that the coupling mechanism is sensitive to the electronic states in the light harvesting complexes. Plasmon-exciton coupling models reveal different coupling strengths depending on the molecular organization and the protein coverage, consistent with strong coupling. Strong coupling was also observed for self-assembling polypeptide maquettes that contain only chlorins. However, it is not observed for monolayers of bacteriochlorophyll, indicating that strong plasmon-exciton coupling is sensitive to the specific presentation of the pigment molecules.

A translation invariant bipolaron in the Holstein model and superconductivity

Large-radius translation invariant (TI) bipolarons are considered in a one-dimensional Holstein molecular chain. Criteria of their stability are obtained. The energy of a translation invariant bipolaron is shown to be lower than that of a bipolaron with broken symmetry. The results obtained are applied to the problem of superconductivity in 1D-systems. It is shown that TI-bipolaron mechanism of Bose-Einstein condensation can support superconductivity even for infinite chain.

Coherent Coupling of WS2 Monolayers with Metallic Photonic Nanostructures at Room Temperature

Room temperature strong coupling of WS2 monolayer exciton transitions to metallic Fabry-Pérot and plasmonic optical cavities is demonstrated. A Rabi splitting of 101 meV is observed for the Fabry-Pérot cavity. The enhanced magnitude and visibility of WS2 monolayer strong coupling is attributed to the larger absorption coefficient, the narrower line width of the A exciton transition, and greater spin-orbit coupling. For WS2 coupled to plasmonic arrays, the Rabi splitting still reaches 60 meV despite the less favorable coupling conditions, and displays interesting photoluminescence features. The unambiguous signature of WS2 monolayer strong coupling in easily fabricated metallic resonators at room temperature suggests many possibilities for combining light-matter hybridization with spin and valleytronics.

Aluminum Nanoantenna Complexes for Strong Coupling between Excitons and Localized Surface Plasmons

We study the optical dynamics in complexes of aluminum nanoantennas coated with molecular J-aggregates and find that they provide an excellent platform for the formation of hybrid exciton-localized surface plasmons. Giant Rabi splitting of 0.4 eV, which corresponds to ∼10 fs energy transfer cycle, is observed in spectral transmittance. We show that the nanoantennas can be used to manipulate the polarization of hybrid states and to confine their mode volumes. In addition, we observe enhancement of the photoluminescence due to enhanced absorption and increase in the local density of states at the exciton-localized surface plasmon energies. With recent emerging technological applications based on strongly coupled light-matter states, this study opens new possibilities to explore and utilize the unique properties of hybrid states over all of the visible region down to ultraviolet frequencies in nanoscale, technologically compatible, integrated platforms based on aluminum.

Strongly Coupled Quantum Heat Machines

Energy conversion of heat into work at the quantum level is modeled by quantum heat machines (QHMs) generally assumed to operate at weak coupling to the baths. This supposition is grounded in the separability principle between systems and allows the derivation of the evolution equation. In the weak coupling regime, the machine's output is limited by the coupling strength, restricting their application. Seeking to overcome this limitation, we analyze QHMs in the virtually unexplored strong coupling regime here, where separability, as well as other standard thermodynamic assumptions, may no longer hold. We show that strongly coupled QHMs may be as efficient as their weakly coupled counterparts. In addition, we find a novel turnover behavior where their output saturates and disappears in the limit of ultrastrong coupling.