Alternant Hydrocarbon Diradicals as Optically Addressable Molecular Qubits.

High-spin molecules allow for bottom-up qubit design and are promising platforms for magnetic sensing and quantum information science. Optical addressability of molecular electron spins has also been proposed in first-row transition-metal complexes via optically detected magnetic resonance (ODMR) mechanisms analogous to the diamond-nitrogen-vacancy color center. However, significantly less progress has been made on the front of metal-free molecules, which can deliver lower costs and milder environmental impacts. At present, most luminescent open-shell organic molecules are π-diradicals, but such systems often suffer from poor ground-state open-shell characters necessary to realize a stable ground-state molecular qubit. In this work, we use alternancy symmetry to selectively minimize radical-radical interactions in the ground state, generating π-systems with high diradical characters. We call them m-dimers, referencing the need to covalently link two benzylic radicals at their meta carbon atoms for the desired symmetry. Through a detailed electronic structure analysis, we find that the excited states of alternant hydrocarbon m-diradicals contain important symmetries that can be used to construct ODMR mechanisms leading to ground-state spin polarization. The molecular parameters are set in the context of a tris(2,4,6-trichlorophenyl)methyl (TTM) radical dimer covalently tethered at the meta position, demonstrating the feasibility of alternant m-diradicals as molecular color centers.

Linear response of molecular polaritons.

In this article, we show that the collective light-matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A-C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics.

Control of Photoswitching Kinetics with Strong Light-Matter Coupling in a Cavity.

Most photochemistry occurs in the regime of weak light-matter coupling, in which a molecule absorbs a photon and then performs photochemistry from its excited state. In the strong coupling regime, enhanced light-matter interactions between an optical field and multiple molecules lead to collective hybrid light-matter states called polaritons. This strong coupling leads to fundamental changes in the nature of the excited states including multi-molecule delocalized excitations, modified potential energy surfaces, and dramatically altered energy levels relative to non-coupled molecules. The effect of strong light-matter coupling on covalent photochemistry has not been well explored. Photoswitches undergo reversible intramolecular photoreactions that can be readily monitored spectroscopically. In this work, we study the effect of strong light-matter coupling on the kinetics of photoswitching within optical cavities. Reproducing prior experiments, photoswitching of spiropyran/merocyanine photoswitches is decelerated in a cavity. Fulgide photoswitches, however, show the opposite effect, with strong coupling accelerating photoswitching. While modified merocyanine switching can be explained by changes in radiative decay rates or the amount of light in the cavity, modified fulgide switching kinetics suggest direct changes to excited-state reaction kinetics.

A path towards single molecule vibrational strong coupling in a Fabry-Pérot microcavity.

Interaction between light and molecular vibrations leads to hybrid light-matter states called vibrational polaritons. Even though many intriguing phenomena have been predicted for single-molecule vibrational strong coupling (VSC), several studies suggest that these effects tend to be diminished in the many-molecule regime due to the presence of dark states. Achieving single or few-molecule vibrational polaritons has been constrained by the need for fabricating extremely small mode volume infrared cavities. In this theoretical work, we propose an alternative strategy to achieve single-molecule VSC in a cavity-enhanced Raman spectroscopy (CERS) setup, based on the physics of cavity optomechanics. We then present a scheme harnessing few-molecule VSC to thermodynamically couple two reactions, such that a spontaneous electron transfer can now fuel a thermodynamically uphill reaction that was non-spontaneous outside the cavity.

Simulating molecular polaritons in the collective regime using few-molecule models.

The study of molecular polaritons beyond simple quantum emitter ensemble models (e.g., Tavis-Cummings) is challenging due to the large dimensionality of these systems and the complex interplay of molecular electronic and nuclear degrees of freedom. This complexity constrains existing models to either coarse-grain the rich physics and chemistry of the molecular degrees of freedom or artificially limit the description to a small number of molecules. In this work, we exploit permutational symmetries to drastically reduce the computational cost of ab initio quantum dynamics simulations for large N. Furthermore, we discover an emergent hierarchy of timescales present in these systems, that justifies the use of an effective single molecule to approximately capture the dynamics of the entire ensemble, an approximation that becomes exact as N → ∞. We also systematically derive finite N corrections to the dynamics and show that addition of k extra effective molecules is enough to account for phenomena whose rates scale as 𝒪(N-k). Based on this result, we discuss how to seamlessly modify existing single-molecule strong coupling models to describe the dynamics of the corresponding ensemble. We call this approach collective dynamics using truncated equations (CUT-E), benchmark it against well-known results of polariton relaxation rates, and apply it to describe a universal cavity-assisted energy funneling mechanism between different molecular species. Beyond being a computationally efficient tool, this formalism provides an intuitive picture for understanding the role of bright and dark states in chemical reactivity, necessary to generate robust strategies for polariton chemistry.

Molecular polariton electroabsorption.

We investigate electroabsorption (EA) in organic semiconductor microcavities to understand whether strong light-matter coupling non-trivially alters their nonlinear optical [[Formula: see text]] response. Focusing on strongly-absorbing squaraine (SQ) molecules dispersed in a wide-gap host matrix, we find that classical transfer matrix modeling accurately captures the EA response of low concentration SQ microcavities with a vacuum Rabi splitting of [Formula: see text] meV, but fails for high concentration cavities with [Formula: see text] meV. Rather than new physics in the ultrastrong coupling regime, however, we attribute the discrepancy at high SQ concentration to a nearly dark H-aggregate state below the SQ exciton transition, which goes undetected in the optical constant dispersion on which the transfer matrix model is based, but nonetheless interacts with and enhances the EA response of the lower polariton mode. These results indicate that strong coupling can be used to manipulate EA (and presumably other optical nonlinearities) from organic microcavities by controlling the energy of polariton modes relative to other states in the system, but it does not alter the intrinsic optical nonlinearity of the organic semiconductor inside the cavity.

Cavity-enabled enhancement of ultrafast intramolecular vibrational redistribution over pseudorotation.

Vibrational strong coupling (VSC) between molecular vibrations and microcavity photons yields a few polaritons (light-matter modes) and many dark modes (with negligible photonic character). Although VSC is reported to alter thermally activated chemical reactions, its mechanisms remain opaque. To elucidate this problem, we followed ultrafast dynamics of a simple unimolecular vibrational energy exchange in iron pentacarbonyl [Fe(CO)5] under VSC, which showed two competing channels: pseudorotation and intramolecular vibrational-energy redistribution (IVR). We found that under polariton excitation, energy exchange was overall accelerated, with IVR becoming faster and pseudorotation being slowed down. However, dark-mode excitation revealed unchanged dynamics compared with those outside of the cavity, with pseudorotation dominating. Thus, despite controversies around thermally activated VSC modified chemistry, our work shows that VSC can indeed alter chemistry through a nonequilibrium preparation of polaritons.

Generalization of the Tavis-Cummings model for multi-level anharmonic systems: Insights on the second excitation manifold.

Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.

Driving chemical reactions with polariton condensates.

When molecular transitions strongly couple to photon modes, they form hybrid light-matter modes called polaritons. Collective vibrational strong coupling is a promising avenue for control of chemistry, but this can be deterred by the large number of quasi-degenerate dark modes. The macroscopic occupation of a single polariton mode by excitations, as observed in Bose-Einstein condensation, offers promise for overcoming this issue. Here we theoretically investigate the effect of vibrational polariton condensation on the kinetics of electron transfer processes. Compared with excitation with infrared laser sources, the vibrational polariton condensate changes the reaction yield significantly at room temperature due to additional channels with reduced activation barriers resulting from the large accumulation of energy in the lower polariton, and the many modes available for energy redistribution during the reaction. Our results offer tantalizing opportunities to use condensates for driving chemical reactions, kinetically bypassing usual constraints of fast intramolecular vibrational redistribution in condensed phase.

Enantioselective Topological Frequency Conversion.

Two molecules are enantiomers if they are nonsuperimposable mirror images of each other. Electric dipole-allowed cyclic transitions |1⟩ → |2⟩ → |3⟩ → |1⟩ obey the symmetry relation OR=-OS, where OR,S = (µ21R,SE21)(µ13R,SE13)(µ32R,SE32) and R and S label the two enantiomers. Herein, we generalize the concept of topological frequency conversion to an ensemble of enantiomers. We show that, within a rotating-frame, the pumping power between fields of frequency ω1 and ω2 is sensitive to enantiomeric excess, P2→1 = ℏ[ω1ω2CLR/(2π)](NR - NS), where Ni is the number of enantiomers i and CLR is an enantiomer-dependent Chern number. Connections with chiroptical microwave spectroscopy are made. Our work provides an underexplored and fertile connection between topological physics and molecular chirality.

Catalysis by Dark States in Vibropolaritonic Chemistry.

Collective strong coupling between a disordered ensemble of N localized molecular vibrations and a resonant optical cavity mode gives rise to two polariton and N-1≫2 dark modes. Thus, experimental changes in thermally activated reaction kinetics due to polariton formation appear entropically unlikely and remain a puzzle. Here we show that the overlooked dark modes, while parked at the same energy as bare molecular vibrations, are robustly delocalized across ∼2-3 molecules, yielding enhanced channels of vibrational cooling, concomitantly catalyzing a chemical reaction. As an illustration, we theoretically show an ≈50% increase in an electron transfer rate due to enhanced product stabilization. The reported effects can arise when the homogeneous linewidths of the dark modes are smaller than their energy spacings.

Microcavity-like exciton-polaritons can be the primary photoexcitation in bare organic semiconductors.

Strong-coupling between excitons and confined photonic modes can lead to the formation of new quasi-particles termed exciton-polaritons which can display a range of interesting properties such as super-fluidity, ultrafast transport and Bose-Einstein condensation. Strong-coupling typically occurs when an excitonic material is confided in a dielectric or plasmonic microcavity. Here, we show polaritons can form at room temperature in a range of chemically diverse, organic semiconductor thin films, despite the absence of an external cavity. We find evidence of strong light-matter coupling via angle-dependent peak splittings in the reflectivity spectra of the materials and emission from collective polariton states. We additionally show exciton-polaritons are the primary photoexcitation in these organic materials by directly imaging their ultrafast (5 × 106 m s-1), ultralong (~270 nm) transport. These results open-up new fundamental physics and could enable a new generation of organic optoelectronic and light harvesting devices based on cavity-free exciton-polaritons.

Nonequilibrium effects of cavity leakage and vibrational dissipation in thermally activated polariton chemistry.

In vibrational strong coupling (VSC), molecular vibrations strongly interact with the modes of an optical cavity to form hybrid light-matter states known as vibrational polaritons. Experiments show that the kinetics of thermally activated chemical reactions can be modified by VSC. Transition-state theory, which assumes that internal thermalization is fast compared to reactive transitions, has been unable to explain the observed findings. Here, we carry out kinetic simulations to understand how dissipative processes, namely, those introduced by VSC to the chemical system, affect reactions where internal thermalization and reactive transitions occur on similar timescales. Using the Marcus-Levich-Jortner type of electron transfer as a model reaction, we show that such dissipation can change reactivity by accelerating internal thermalization, thereby suppressing nonequilibrium effects that occur in the reaction outside the cavity. This phenomenon is attributed mainly to cavity decay (i.e., photon leakage), but a supporting role is played by the relaxation between polaritons and dark states. When nonequilibrium effects are already suppressed in the bare reaction (the reactive species are essentially at internal thermal equilibrium throughout the reaction), we find that reactivity does not change significantly under VSC. Connections are made between our results and experimental observations.

Active Plasmonics and Active Chiral Plasmonics through Orientation-Dependent Multipolar Interactions.

While most active plasmonic efforts focus on responsive metamaterials to modulate optical response, we present a simple alternative based on applied orientation control that can likely be implemented for many passive plasmonic materials. Passive plasmonic motifs are simpler to prepare but cannot be altered postfabrication. We show that such systems can be easily manipulated through substrate orientation control to generate both active plasmonic and active chiral plasmonic responses. Using gold nanocrescents as our model platform, we demonstrate tuning of optical extinction from -21% to +36% at oblique incidence relative to normal incidence. Variation of substrate orientation in relation to incident polarization is also demonstrated to controllably switch chiroptical handedness (e.g., Δg = ± 0.55). These active plasmonic responses arise from the multipolar character of resonant modes. In particular, we correlate magnetoelectric and dipole-quadrupole polarizabilities with different light-matter orientation-dependence in both near- and far-field localized surface plasmon activity. Additionally, the attribution of far-field optical response to higher-order multipoles highlights the sensitivity offered by these orientation-dependent characterization techniques to probe the influence of localized electromagnetic field gradients on a plasmonic response. The sensitivity afforded by orientation-dependent optical characterization is further observed by the manifestation in both plasmon and chiral plasmon responses of unpredicted structural nanocrescent variance (e.g., left- and right-tip asymmetry) not physically resolved through topographical imaging.

Computational method for highly constrained molecular dynamics of rigid bodies: Coarse-grained simulation of auxetic two-dimensional protein crystals.

The increasing number of protein-based metamaterials demands reliable and efficient theoretical and computational methods to study the physicochemical properties they may display. In this regard, we develop a simulation strategy based on Molecular Dynamics (MD) that addresses the geometric degrees of freedom of an auxetic two-dimensional protein crystal. This model consists of a network of impenetrable rigid squares linked through massless rigid rods. Our MD methodology extends the well-known protocols SHAKE and RATTLE to include highly non-linear holonomic and non-holonomic constraints, with an emphasis on collision detection and response between anisotropic rigid bodies. The presented method enables the simulation of long-time dynamics with reasonably large time steps. The data extracted from the simulations allow the characterization of the dynamical correlations featured by the protein subunits, which show a persistent motional interdependence across the array. On the other hand, non-holonomic constraints (collisions between subunits) increase the number of inhomogeneous deformations of the network, thus driving it away from an isotropic response. Our work provides the first long-timescale simulation of the dynamics of protein crystals and offers insights into promising mechanical properties afforded by these materials.

Polaritonic normal modes in transition state theory.

A series of experiments demonstrates that strong light-matter coupling between vibrational excitations in isotropic solutions of molecules and resonant infrared optical microcavity modes leads to modified thermally activated kinetics. However, Galego et al. [Phys. Rev. X 9, 021057 (2019)] recently demonstrated that, within transition state theory, effects of strong light-matter coupling with reactive modes are mostly electrostatic and essentially independent of light-matter resonance or even of the formation of vibrational polaritons. To analyze this puzzling theoretical result in further detail, we revisit it under a new light, invoking a normal mode analysis of the transition state and reactant configurations for an ensemble of an arbitrary number of molecules in a cavity, obtaining simple analytical expressions that produce similar conclusions as Feist. While these effects become relevant in optical microcavities if the molecular dipoles are anisotropically aligned, or in cavities with extreme confinement of the photon modes, they become negligible for isotropic solutions in microcavities. It is concluded that further studies are necessary to track the origin of the experimentally observed kinetics.

Intermolecular vibrational energy transfer enabled by microcavity strong light-matter coupling.

Selective vibrational energy transfer between molecules in the liquid phase, a difficult process hampered by weak intermolecular forces, is achieved through polaritons formed by strong coupling between cavity photon modes and donor and acceptor molecules. Using pump-probe and two-dimensional infrared spectroscopy, we found that the excitation of the upper polariton, which is composed mostly of donors, can efficiently relax to the acceptors within ~5 picoseconds. The energy-transfer efficiency can be further enhanced by increasing the cavity lifetime, suggesting that the energy transfer is a polaritonic process. This vibrational energy-transfer pathway opens doors for applications in remote chemistry, sensing mechanisms, and vibrational polariton condensation.

Manipulating molecules with strong coupling: harvesting triplet excitons in organic exciton microcavities.

Exciton-polaritons are quasiparticles with mixed photon and exciton character that demonstrate rich quantum phenomena, novel optoelectronic devices and the potential to modify chemical properties of materials. Organic materials are of current interest as active materials for their ability to sustain exciton-polaritons even at room temperature. However, within organic optoelectronic devices, it is often the 'dark' spin-1 triplet excitons that dominate operation. These triplets have been largely ignored in treatments of polaritons, which instead only consider the role of states that directly and strongly interact with light. Here we demonstrate that these 'dark' states can also play a major role in polariton dynamics, observing polariton population transferred directly from the triplet manifold via triplet-triplet annihilation. The process leads to polariton emission that is longer-lived (>µs) even than exciton emission in bare films. This enhancement is directly linked to spin-2 triplet-pair states, which are formed in films and microcavities by singlet fission or triplet-triplet annihilation. Such high-spin multiexciton states are generally non-emissive and cannot directly couple to light, yet the formation of polaritons creates for them entirely new radiative decay pathways. This is possible due to weak mixing between singlet and triplet-pair manifolds, which - in the strong coupling regime - enables direct interaction between the bright polariton states and those that are formally non-emissive. Our observations offer the enticing possibility of using polaritons to harvest or manipulate population from states that are formally dark.

Correction: Polariton chemistry: controlling molecular dynamics with optical cavities.

[This corrects the article DOI: 10.1039/C8SC01043A.].