Harnessing multi-mode optical structure for chemical reactivity

TL;DR

This work probes how a few discrete cavity modes, rather than a single mode, reshape chemical reactivity in vibrational polariton chemistry. Using numerically exact HEOM+TTNS simulations of a molecule in a multimode planar cavity, it reveals two main mechanisms for enhanced reactivity: (i) near-degenerate neighboring modes hybridize with a rate-decisive vibration when the free spectral range $\Delta$ is comparable to the single-mode Rabi splitting $\Omega_{\rm R}$, creating alternative reaction pathways, and (ii) molecular anharmonicity allows distinct vibrational transitions to couple to different cavity modes, enabling cascade multi-photon processes and non-additive rate increases. The results show cooperative, mode–mode interference effects; while in many regimes adding modes boosts rates, there are parameter windows where additional modes suppress reactivity, and damping or bath sharing can erode the multimode signatures. These findings provide design principles for polaritonic catalysis by tailoring multimode structures and call for advanced theoretical tools beyond Fermi’s Golden Rule to capture explicit polariton dynamics in multimode settings.

Abstract

The prospect of controlling chemical reactivity using frequency-tunable optical microcavities has materialized over the past decade, evolving into a fascinating yet challenging new field of polaritonic chemistry, a multidisciplinary domain at the intersection of quantum optics, chemical dynamics, and non-equilibrium many-body physics. While most theoretical efforts to date have focused on single-mode cavities, practical implementations in polaritonic chemistry typically involve planar optical cavities that support a series of equally spaced photon modes, determined by the cavity geometry. In this work, we present a numerically exact, fully quantum-mechanical study of chemical reactions in few-mode cavities, revealing two key scenarios by which multi-mode effects can enhance cavity-modified reactivity. The first scenario emerges when the free spectral range is comparable to the single-mode Rabi splitting. In such cases, hybridization between a rate-decisive molecular vibration and a central resonant cavity mode reshapes the resonance landscape, enabling additional reaction pathways mediated by adjacent cavity modes. The second scenario exploits the intrinsic anharmonicity of molecular vibrations, which gives rise to multiple dipole-allowed transitions with distinct energies. Under multi-mode strong coupling, where different cavity modes individually resonate with these distinct transitions, multi-photon processes involving sequential absorption across multiple modes become accessible. This leads to a nontrivial and non-additive rate enhancement via cascade-like vibrational ladder climbing. Together, these findings offer new strategies for tailoring chemical reactivity by harnessing the structural richness of multi-mode structure, offering valuable insights for optimal experimental designs in polaritonic catalysis.

Figures (17)

• Figure 1: a) Sketch of an optical cavity with a path length of $L$ that supports multiple discrete cavity modes. b) Graphical representation of the TTNS decomposition for the extended wavefunction $|\Psi(t)\rangle$ for an open quantum system model describing chemical reactions in optical cavity within the HEOM framework. Each colored node with an open leg in the diagram represents a low-rank tensor related to a physical DoF (red: molecule, yellow: two cavity modes, green: solvent, and blue: cavity baths). Gray node is a rank-3 connecting tensor, introduced for improving the numerical efficiency. Here, both the solvent and cavity baths are represented by four Padé poles, i.e., $P=4$ in Eq. (\ref{['timecorrelation']}). A connected leg represents a shared virtual index between two nodes, which runs from $1$ to $D_{i}$. The maximal bond dimension is denoted as $D_{\rm max}$.
• Figure 2: a) Potential energy surface for the symmetric double-well model as defined in Eq. (\ref{['PES']}) with $E_{\rm b}=2250\,\mathrm{cm}^{-1}$ and $a=44.4$ a.u. for two different reduced masses $M$. The energies and the wavefunctions of localized vibrational states below the reaction barriers are shown, respectively, in each panel. b) Absorption profile of a single molecule outside the cavity for the corresponding model shown to the left. The vertical lines indicate the energy gaps of the dipole-allowed vibrational transitions in the bare molecule, as marked by the double-headed arrows in a).
• Figure 3: a) Rate modification (ratio $k^1_{\mathrm c}/k_{\mathrm{o}}$) for Model I in a single-mode cavity as a function of the cavity frequency $\omega_{\mathrm{c}}$. b-c) Rate modification ((ratio $k^2_{\mathrm c}/k_{\mathrm{o}}$)) for Model I as a function of the FSR $\Delta$ in a two-mode cavity, where $\omega_{\mathrm c}$ is the frequency for the central cavity mode, and $\omega'_{\mathrm c}=\omega_{\mathrm c}+\Delta$ for a neighboring mode. The light-matter coupling strength is set to $\eta_1=\eta_2=0.00125~$ a.u.
• Figure 4: Absorption profiles of a single molecule (Model I) in a single-mode cavity (left column) with three different cavity frequencies, and a two-mode cavity (right column) with a central cavity frquency at $\omega_{\mathrm{c}}=1185\mathrm{cm}^{-1}$ and three different neighboring cavity frequencies $\omega'_{\rm c}$. The light-matter coupling strength is set to $\eta_1=\eta_2=0.00125~$ a.u.
• Figure 5: a) Schematic illustration of the hybridization between a molecular transition and the first cavity mode, forming two polaritonic states, which modifies the resonant conditions for the second cavity mode. b) Reaction mechanism in a two-mode cavity, which is responsible for the additional rate enhancement observed in Fig. \ref{['fig3:rates_model1']} b)-d).