Volume 13, Issue 14 - Special Issue: Strong Coupling of Organic Molecules

The investigation of strong coupling between light and matter is an important field of research. Its significance arises not only from the emergence of a plethora of intriguing chemical and physical phenomena, often novel and unexpected, but also from its provision of important tool sets for the design of core components for novel chemical, electronic, and photonic devices such as quantum computers, lasers, amplifiers, modulators, sensors and more. Strong coupling has been demonstrated for various material systems and spectral regimes, each exhibiting unique features and applications. In this perspective, we will focus on a sub-field of this domain of research and discuss the strong coupling between metamaterials and photonic cavities at THz frequencies . The metamaterials, themselves electromagnetic resonators, serve as “artificial atoms”. We provide a concise overview of recent advances and outline possible research directions in this vital and impactful field of interdisciplinary science.

We provide a simple method that enables readily acquired experimental data to be used to predict whether or not a candidate molecular material may exhibit strong coupling. Specifically, we explore the relationship between the hybrid molecular/photonic (polaritonic) states and the bulk optical response of the molecular material. For a given material, this approach enables a prediction of the maximum extent of strong coupling (vacuum Rabi splitting), irrespective of the nature of the confined light field. We provide formulae for the upper limit of the splitting in terms of the molar absorption coefficient, the attenuation coefficient, the extinction coefficient (imaginary part of the refractive index) and the absorbance. To illustrate this approach, we provide a number of examples, and we also discuss some of the limitations of our approach.

The vacuum Rabi splitting (VRS) in molecular polaritons stands as a fundamental measure of collective light–matter coupling. Despite its significance, the impact of molecular disorder on VRS is not fully understood yet. This study delves into the complexities of VRS amidst various distributions and degrees of disorder. Our analysis provides precise analytical expressions for linear absorption, transmission, and reflection spectra, along with a “sum” rule, offering a straightforward protocol for extracting accurate collective light–matter coupling values from experimental data. Importantly, our study cautions against directly translating large VRS to the onset of ultrastrong coupling regime. Furthermore, for rectangular disorder, we witness the emergence of narrow side bands alongside a broad central peak, indicating an extended coherence lifetime even in the presence of substantial disorder. These findings not only enhance our understanding of VRS in disordered molecular systems but also open avenues for achieving prolonged coherence lifetimes between the cavity and molecules via the interplay of collective coupling and disorder.

Hybridisation of the cavity modes and the excitons to polariton states together with the coupling to the vibrational modes determine the linear optical properties of organic semiconductors in microcavities. In this article we compute the refractive index for such system using the Holstein–Tavis–Cummings model and determine then the linear optical properties using the transfer matrix method. We first extract the parameters for the exciton in our model from fitting to experimentally measured absorption of a 2,7-bis[9,9-di(4-methylphenyl)-fluoren-2-yl]-9,9-di(4-methylphenyl) fluorene (TDAF) molecular thin film. Then we compute the reflectivity of such a thin film in a metal clad microcavity system by including the dispersive microcavity mode to the model. We compute susceptibility of the model systems evolving just a single state vector by using the non-Markovian quantum state diffusion. The computed location and height of the lower and upper polaritons agree with the experiment within the estimated errorbars for small angles ( ≤ 30 ° ) $(\le 30{}^{\circ})$ . For larger angles the location of the polariton resonances are within the estimated error.

Exploring the non-Hermitian properties of semiconductor materials for optical applications is at the forefront of photonic research. However, the selection of appropriate systems to implement such photonic devices remains a topic of debate. In this work, we demonstrate that a perovskite crystal, characterized by its easy and low-cost manufacturing, when placed between two distributed Bragg reflectors with an air gap, can form a natural double microcavity. This construction shows promising properties for the realisation of novel, tunable non-Hermitian photonic devices through strong light–matter coupling. We reveal that such a system exhibits double-coupled polariton modes with dispersion including multiple inflection points. Owing to its non-Hermiticity, our system exhibits nonreciprocal properties and allows for the observation of exceptional points. Our experimental studies are in agreement with the theoretical analysis based on coupled mode theory and calculations based on transfer matrix method.

The realization of higher coupling strengths between coupled resonant modes enables exploration of compelling phenomena in diverse fields of physics and chemistry. In this study, we focus on the modal coupling between localized surface plasmon resonance (LSPR) of Au nanoparticles (Au-NPs) and Fabry–Pérot mode (p-NiO/Au film). The effects of nanoparticle size, projected surface coverage (PSC), interparticle distance (IPD), and arrangement to the coupling strength between the two modes are theoretically investigated using finite-difference time-domain (FDTD) method. Au-NPs/p-NiO/Au film (ANA) nanostructures with NPs size of 10 nm, 30 nm, and 50 nm are considered. Numerical calculations point to larger size and higher projected surface coverage (also smaller IPD) of NPs as pre-eminent factors in enhancing the strength of modal coupling. ANA nanostructure with NPs size of 30 nm (ANA-30) and 50 nm (ANA-50) are experimentally fabricated via a facile air–liquid interface self-assembly. The fabricated nanodevices exhibit immense Rabi splitting energies of 655 meV (ANA-30) and 770 meV (ANA-50), and thus fulfill the ultrastrong coupling condition with remarkable splitting energy to bare (plasmon) energy ratio of 0.35 (ANA-30) and 0.4 (ANA-50). The physical insights presented in this study, together with the simple and scalable fabrication process, establish a viable approach to realize stronger coupling between LSPR and Fabry–Pérot mode in metal NPs/dielectric/metal film systems. This will be vital to take advantage of the promising performance enhancements of plasmonic-based nanostructures under strongly coupled regimes in areas such as solar to fuel conversion, sensing, opto-electronics, and quantum applications.

We discuss the possibility of self-hybridisation in high-index dielectric nanoparticles, where Mie modes of electric or magnetic type can couple to the interband transitions of the material, leading to spectral anticrossings. Starting with an idealised system described by moderately high constant permittivity with a narrow Lorentzian, in which self-hybridisation is visible for both plane-wave and electron-beam excitation, we embark on a quest for realistic systems where this effect should be visible. We explore a variety of spherical particles made of traditional semiconductors such as Si, GaAs, and GaP. With the effect hardly discernible, we identify two major causes hindering observation of self-hybridisation: the very broad spectral fingerprints of interband transitions in most candidate materials, and the significant overlap between electric and magnetic Mie modes in nanospheres. We thus depart from the spherical shape, and show that interband–Mie hybridisation is indeed feasible in the example of GaAs cylinders, even with a simple plane-wave source. This so-far unreported kind of polariton has to be considered when interpreting experimental spectra of Mie-resonant nanoparticles and assigning modal characters to specific features. On the other hand, it has the potential to be useful for the characterisation of the optical properties of dielectric materials, through control of the hybridisation strength via nanoparticle size and shape, and for applications that exploit Mie resonances in metamaterials, highly-directional antennas, or photovoltaics.

Strong coupling between the molecular vibrations and electromagnetic fields of light confined to an infrared cavity leads to the formation of vibro-polaritons – quasi-particles thought to provide the means to control the rates of chemical reactions inside a dark cavity. Despite the mechanisms indicating how vibrational coupling to the vacuum fields can affect the reaction rates are still not well understood, it has been recently demonstrated that the formation of the polariton states alters the ultrafast relaxation dynamics of the strongly coupled system. The relaxation dynamics in molecules, which is known to be important for the chemical reactivity, is directed by anharmonic couplings involving multiple intra- and inter-molecular vibrational degrees of freedom. However, the impact of the molecular anharmonicity on the polariton states remains elusive. Some theoretical models, employed to interpret the experimental observations, assume that vibrational polaritons are harmonic. Others assume a certain anharmonicity of vibro-polaritons; however, to date, it has not been experimentally determined. Herein, we performed double-quantum two-dimensional third-order nonlinear infrared spectroscopy of the carbonyl stretching (C=O) vibrational modes in a thin film of polymethyl methacrylate polymer (PMMA) strongly coupled to the surface lattice resonances of the periodic arrays of half-wavelength infrared disk antennas. We found that, indeed, the mechanical anharmonicity of polaritons is very small. Quantitatively, our results place an upper bound on a polariton mechanical anharmonicity of 2 cm −1 , compared with that of the C=O mode in a PMMA film of 15 cm −1 . Thus, our results support previous assumptions regarding the harmonic character of vibro-polaritons.

The short exciton diffusion length in organic semiconductors results in a strong dependence of the conversion efficiency of organic photovoltaic (OPV) cells on the morphology of the donor-acceptor bulk-heterojunction blend. Strong light–matter coupling provides a way to circumvent this dependence by combining the favorable properties of light and matter via the formation of hybrid exciton–polaritons. By strongly coupling excitons in P3HT-C 60 OPV cells to Fabry–Perot optical cavity modes, exciton-polaritons are formed with increased propagation lengths. We exploit these exciton–polaritons to enhance the internal quantum efficiency of the cells, determined from the external quantum efficiency and the absorptance. Additionally, we find a consistent decrease in the Urbach energy for the strongly coupled cells, which indicates the reduction of energetic disorder due to the delocalization of exciton–polaritons in the optical cavity.

Optical control is achieved on the excited state energy transfer between spatially separated donor and acceptor molecules, both coupled to the same optical mode of a cavity. The energy transfer occurs through the formed hybrid polaritons and can be switched on and off by means of ultraviolet and visible light. The control mechanism relies on a photochromic component used as donor, whose absorption and emission properties can be varied reversibly through light irradiation, whereas in-cavity hybridization with acceptors through polariton states enables a 6-fold enhancement of acceptor/donor contribution to the emission intensity with respect to a reference multilayer. These results pave the way for synthesizing effective gating systems for the transport of energy by light, relevant for light-harvesting and light-emitting devices, and for photovoltaic cells.

Excitation energy transport can be significantly enhanced by strong light–matter interactions. In the present work, we explore intriguing features of coherent transient exciton wave packet dynamics on a lossless disordered polaritonic wire. Our main results can be understood in terms of the effective exciton group velocity, a new quantity we obtain from the polariton dispersion. Under weak and moderate disorder, we find that the early wave packet spread velocity is controlled by the overlap of the initial exciton momentum distribution and its effective group velocity. Conversely, when disorder is stronger, the initial state is nearly irrelevant, and red-shifted cavities support excitons with greater mobility. Our findings provide guiding principles for optimizing ultrafast coherent exciton transport based on the magnitude of disorder and the polariton dispersion. The presented perspectives may be valuable for understanding and designing new polaritonic platforms for enhanced exciton energy transport.

Modifying the energy landscape of existing molecular emitters is an attractive challenge with favourable outcomes in chemistry and organic optoelectronic research. It has recently been explored through strong light–matter coupling studies where the organic emitters were placed in an optical cavity. Nonetheless, a debate revolves around whether the observed change in the material properties represents novel coupled system dynamics or the unmasking of pre-existing material properties induced by light–matter interactions. Here, for the first time, we examined the effect of strong coupling in polariton organic light-emitting diodes via time-resolved electroluminescence studies. We accompanied our experimental analysis with theoretical fits using a model of coupled rate equations accounting for all major mechanisms that can result in delayed electroluminescence in organic emitters. We found that in our devices the delayed electroluminescence was dominated by emission from trapped charges and this mechanism remained unmodified in the presence of strong coupling.

The emerging field of molecular cavity polaritons has stimulated a surge of experimental and theoretical activities and presents a unique opportunity to develop the many-body simulation methodology. This paper presents a numerical scheme for the extraction of key kinetic information of lossy cavity polaritons based on the transfer tensor method (TTM). Steady state, relaxation timescales, and oscillatory phenomena can all be deduced directly from a set of transfer tensors without the need for long-time simulation. Moreover, we generalize TTM to disordered systems by sampling dynamical maps and achieve fast convergence to disordered-averaged dynamics using a small set of realizations. Together, these techniques provide a toolbox for characterizing the interplay of cavity loss, disorder, and cooperativity in polariton relaxation and allow us to predict unusual dependences on the initial excitation state, photon decay rate, strength of disorder, and the type of cavity models. Thus, using the example of cavity polaritons, we have demonstrated significant potential in the use of the TTM toward both the efficient computation of long-time polariton dynamics and the extraction of crucial kinetic information about polariton relaxation from a small set of short-time trajectories.

Molecular polaritons, hybrid light-matter states resulting from strong cavity coupling of optical transitions, may provide a new route to guide chemical reactions. However, demonstrations of cavity-modified reactivity in clean benchmark systems are still needed to clarify the mechanisms and scope of polariton chemistry. Here, we use transient absorption to observe the ultrafast dynamics of CN radicals interacting with a cyclohexane ( c -C 6 H 12 ) and chloroform (CHCl 3 ) solvent mixture under vibrational strong coupling of a C–H stretching mode of c- C 6 H 12 . By modulating the c -C 6 H 12 :CHCl 3 ratio, we explore how solvent complexation and hydrogen (H)-abstraction processes proceed under collective cavity coupling strengths ranging from 55 to 85 cm −1 . Reaction rates remain unchanged for all extracavity, on-resonance, and off-resonance cavity coupling conditions, regardless of coupling strength. These results suggest that insufficient vibrational cavity coupling strength may not be the determining factor for the negligible cavity effects observed previously in H-abstraction reactions of CN with CHCl 3 .

We present a theory that explains the resonance effect of the vibrational strong coupling (VSC) modified reaction rate constant at the normal incidence of a Fabry–Pérot (FP) cavity. This analytic theory is based on a mechanistic hypothesis that cavity modes promote the transition from the ground state to the vibrational excited state of the reactant, which is the rate-limiting step of the reaction. This mechanism for a single molecule coupled to a single-mode cavity has been confirmed by numerically exact simulations in our recent work in [J. Chem. Phys. 159, 084104 (2023)]. Using Fermi’s golden rule (FGR), we formulate this rate constant for many molecules coupled to many cavity modes inside a FP microcavity. The theory provides a possible explanation for the resonance condition of the observed VSC effect and a plausible explanation of why only at the normal incident angle there is the resonance effect, whereas, for an oblique incidence, there is no apparent VSC effect for the rate constant even though both cases generate Rabi splitting and forming polariton states. On the other hand, the current theory cannot explain the collective effect when a large number of molecules are collectively coupled to the cavity, and future work is required to build a complete microscopic theory to explain all observed phenomena in VSC.

In this paper, we develop quantum dynamical methods capable of treating the dynamics of chemically reacting systems in an optical cavity in the vibrationally strong-coupling (VSC) limit at finite temperatures and in the presence of a dissipative solvent in both the few and many molecule limits. In the context of two simple models, we demonstrate how reactivity in the collective VSC regime does not exhibit altered rate behavior in equilibrium but may exhibit resonant cavity modification of reactivity when the system is explicitly out of equilibrium. Our results suggest experimental protocols that may be used to modify reactivity in the collective regime and point to features not included in the models studied, which demand further scrutiny.

Polariton thermalization is a key process in achieving light–matter Bose–Einstein condensation, spanning from solid-state semiconductor microcavities at cryogenic temperatures to surface plasmon nanocavities with molecules at room temperature. Originated from the matter component of polariton states, the microscopic mechanisms of thermalization are closely tied to specific material properties. In this work, we investigate polariton thermalization in strongly-coupled molecular systems. We develop a microscopic theory addressing polariton thermalization through electron-phonon interactions (known as exciton-vibration coupling) with low-energy molecular vibrations. This theory presents a simple analytical method to calculate the temperature-dependent polariton thermalization rate, utilizing experimentally accessible spectral properties of bare molecules, such as the Stokes shift and temperature-dependent linewidth of photoluminescence, in conjunction with well-known parameters of optical cavities. Our findings demonstrate qualitative agreement with recent experimental reports of nonequilibrium polariton condensation in both ground and excited states, and explain the thermalization bottleneck effect observed at low temperatures. This study showcases the significance of vibrational degrees of freedom in polariton condensation and offers practical guidance for future experiments, including the selection of suitable material systems and cavity designs.

Exciton–polariton condensates, due to their nonlinear and coherent characteristics, have been employed to construct spin Hamiltonian lattices for potentially studying spin glass, critical dephasing, and even solving optimization problems. Here, we report the room-temperature polariton condensation and polaritonic soft-spin XY Hamiltonian lattices in an organic–inorganic halide perovskite microcavity. This is achieved through the direct integration of high-quality single-crystal samples within the cavity. The ferromagnetic and antiferromagnetic couplings in both one- and two-dimensional condensate lattices have been observed clearly. Our work shows a nonlinear organic–inorganic hybrid perovskite platform for future investigations as polariton simulators.

Optoelectronic and spinoptronic technologies benefit from flexible and tunable coherent light sources combining the best properties of nano- and material-engineering to achieve favorable properties such as chiral lasing and low threshold nonlinearities. In this work we demonstrate an electrically wavelength- and polarization-tunable room temperature polariton laser due to emerging photonic spin–orbit coupling. For this purpose, we design an optical cavity filled with both birefringent nematic liquid crystal and an inorganic perovskite. Our versatile growth method of single CsPbBr 3 inorganic perovskite crystals in polymer templates allows us to reach strong light–matter coupling and pump-induced condensation of exciton–polaritons resulting in coherent emission of light. The sensitivity of the liquid crystal to external voltage permits electrical tuning of the condensate energy across 7 nm; its threshold power, allowing us to electrically switch it on and off; and its state of polarization sweeping from linear to locally tilted circularly polarized emission.

The full information about the interaction between a quantum emitter and an arbitrary electromagnetic environment is encoded in the so-called spectral density. We present an approach for describing such interaction in any coupling regime, providing a Lindblad-like master equation for the emitter dynamics when coupled to a general nanophotonic structure. Our framework is based on the splitting of the spectral density into two terms. On the one hand, a spectral density responsible for the non-Markovian and strong-coupling-based dynamics of the quantum emitter. On the other hand, a residual spectral density including the remaining weak-coupling terms. The former is treated nonperturbatively with a collection of lossy interacting discrete modes whose parameters are determined by a fit to the original spectral density in a frequency region encompassing the quantum emitter transition frequencies. The latter is treated perturbatively under a Markovian approximation. We illustrate the power and validity of our approach through numerical simulations in three different setups, thus offering a variety of scenarios for a full test, including the ultra-strong coupling regime.

Lasers are ubiquitous for information storage, processing, communications, sensing, biological research and medical applications. To decrease their energy and materials usage, a key quest is to miniaturise lasers down to nanocavities. Obtaining the smallest mode volumes demands plasmonic nanocavities, but for these, gain comes from only a single or few emitters. Until now, lasing in such devices was unobtainable due to low gain and high cavity losses. Here, we demonstrate a form of ‘few emitter lasing’ in a plasmonic nanocavity approaching the single-molecule emitter regime. The few-emitter lasing transition significantly broadens, and depends on the number of molecules and their individual locations. We show this non-standard few-emitter lasing can be understood by developing a theoretical approach extending previous weak-coupling theories. Our work paves the way for developing nanolaser applications as well as fundamental studies at the limit of few emitters.

Placing a material inside an optical cavity can enhance transport of excitation energy by hybridizing excitons with confined light modes into polaritons, which have a dispersion that provides these light–matter quasi-particles with low effective masses and very high group velocities. While in experiments, polariton propagation is typically initiated with laser pulses, tuned to be resonant either with the polaritonic branches that are delocalized over many molecules, or with an uncoupled higher-energy electronic excited state that is localized on a single molecule, practical implementations of polariton-mediated exciton transport into devices would require operation under low-intensity incoherent light conditions. Here, we propose to initiate polaritonic exciton transport with a photo-acid, which upon absorption of a photon in a spectral range not strongly reflected by the cavity mirrors, undergoes ultra-fast excited-state proton transfer into a red-shifted excited-state photo-product that can couple collectively with a large number of suitable dye molecules to the modes of the cavity. By means of atomistic molecular dynamics simulations we demonstrate that cascading energy from a photo-excited donor into the strongly coupled acceptor-cavity states via a photo-chemical reaction can indeed induce long-range polariton-mediated exciton transport.

It remains unclear how the collective strong coupling of cavity-confined photons to the electronic transitions of molecular chromophore leverages the distinct properties of the polaritonic constituents for future technologies. In this study, we design, fabricate, and characterize multiple types of Fabry-Pérot (FP) mirco-resonators containing copper(II) tetraphenyl porphyrin (CuTPP) to show how cavity polariton formation affects radiative relaxation processes in the presence of substantial non-Condon vibronic coupling between two of this molecule’s excited electronic states. Unlike the prototypical enhancement of Q state radiative relaxation of CuTPP in a FP resonator incapable of forming polaritons, we find the light emission processes in multimode cavity polariton samples become enhanced for cavity-exciton energy differences near those of vibrations known to mediate non-Condon vibronic coupling. We propose the value of this detuning is consistent with radiative relaxation of Herzberg-Teller polaritons into collective molecular states coupled to the cavity photon coherently. We contrast the feature stemming from light emission from the HT polariton state with those that occur due to polariton-enhanced light absorption. Our results demonstrate the landscape of molecular and photonic interactions enabled by cavity polariton formation using complex chromophores and how researchers can design resonators to leverage these interactions to characterize and control polaritonic properties.