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.

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.

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.

Resonant catalysis of thermally activated chemical reactions with vibrational polaritons.

Interaction between light and matter results in new quantum states whose energetics can modify chemical kinetics. In the regime of ensemble vibrational strong coupling (VSC), a macroscopic number [Formula: see text] of molecular transitions couple to each resonant cavity mode, yielding two hybrid light-matter (polariton) modes and a reservoir of [Formula: see text] dark states whose chemical dynamics are essentially those of the bare molecules. This fact is seemingly in opposition to the recently reported modification of thermally activated ground electronic state reactions under VSC. Here we provide a VSC Marcus-Levich-Jortner electron transfer model that potentially addresses this paradox: although entropy favors the transit through dark-state channels, the chemical kinetics can be dictated by a few polaritonic channels with smaller activation energies. The effects of catalytic VSC are maximal at light-matter resonance, in agreement with experimental observations.