Cavity Control of Strongly Correlated Electrons Beyond Resonant Coupling

Abstract

Interfacing materials with electromagnetic cavities offers a route to modify equilibrium properties through structured vacuum fluctuations. The coupling of light with correlated electrons lacks a characteristic energy scale, making vacuum induced modifications of such systems inherently off-resonant and sensitive to the full photon mode structure. Here, we present a non-perturbative calculation of the cavity induced modification of the magnetic exchange interaction $J$ of the half-filled Hubbard model, including all cavity modes and with parameters determined from first principles. We show that the strength of the modification is controlled by a generalized Purcell factor, proportional to the frequency integrated photonic density of states. This result identifies polaritonic surface cavities as promising platforms to modify correlated systems, while standard Fabry-Pérot resonators produce negligible effects due to spectral weight cancellations upon integration. To perform the calculation, we develop a consistent quantization scheme for materials coupled to a dielectric substrate, in the Coulomb gauge, which reveals a competition between static Coulomb screening and dynamical effects arising from the vector potential. Including both effects is essential to obtain even qualitatively correct predictions. For a gold substrate the light-matter interactions lead to a net enhancement of $J$, whose magnitude is large enough to be observable in two-magnon Raman spectroscopy. Our framework establishes a concrete design principle linking cavity geometry to material response in the off-resonant regime, which will guide future experimental and theoretical explorations.

Figures (11)

• Figure 1: Surface cavity interacting with a strongly correlated material. The hybridization of substrate (blue) excitations with the electromagnetic field yields exponentially localized polaritonic modes at the vacuum-dielectric interface. The coupling of longitudinal and transverse electromagnetic field components to a correlated material (red) leads to an intricate interplay that can produce strong modifications of magnetic exchange interactions.
• Figure 2: Planar cavity dressed magnetic exchange for a Fabry-Perot (FP) cavity with perfect mirrors separated by distance $d$ (inset, top panel) that interacts with a material placed at the midpoint $z = d/2$. (a) Photonic density of states [\ref{['eq:photonic_density_of_states']}] at the cavity center for a FP resonator (purple) and free space (black) in the thermodynamic limit $L_\parallel \to \infty$. The oscillatory cavity PDOS nearly averages to zero over each resonance interval. (b) Relative modification of magnetic exchange [\ref{['eq:resum_J']}] as a function of cavity mirror distance $d$ and fundamental cavity resonance energy $\hbar \omega\textunderscore c$ (top axis) for $a_{ij} = 6\;$Å and $U = 5\;$eV. The full calculation (red) follows a $d^{-3}$ scaling, showing excellent agreement with the perturbative limit (blue, \ref{['eq:resum_taylor_g_eff']}). The gray region ($d \lesssim 0.1~\mu\rm{m}$) marks the breakdown of the perfect-conductor approximation, where $\omega\textunderscore c$ approaches the plasma frequency of typical metals. Predicted modifications remain below current experimental resolution.
• Figure 3: Surface cavity dressed magnetic exchange for a material at a distance $z$ above a gold substrate (top panel inset), modeled via a Lorentzian dielectric function $\varepsilon(\omega)$ with plasma frequency $\hbar \omega\textunderscore p = 9.45$ eV [\ref{['eq:quant_surface_dielectric']}]. (a) Photonic density of states [\ref{['eq:photonic_density_of_states']}] of the gold substrate (purple) and in free space (black; nearly zero on this scale) in the thermodynamic limit $L_\parallel \to \infty$, evaluated at $z = 10~$nm above the substrate. The exponentially localized surface mode produces a strongly peaked enhancement at the limit frequency $\omega_\infty$ [\ref{['eq:quant_surface_limit_freq']}]. (b) Contribution-resolved relative modification of the magnetic exchange [\ref{['eq:resum_J']}] as a function of substrate distance $z$ for $a_{ij} = 6\;$Å and $U = 5\;$eV. Result from PDOS in the top panel indicated by the color-matched arrow. The dynamical dressing via the vector potential (red) suppresses $J$, while the static screening (blue) enhances it. The single-mode approximation (black dashed) accurately captures the dynamical contribution. Both mechanisms scale as $z^{-3}$, leading to strong cancellations and net effect (green) with a percent-level enhancement at nanometer distances. The gray region ($z < 1~\rm{nm}$) marks the breakdown of the macroscopic dielectric description.
• Figure 4: Magnon signatures of cavity renormalization. (a) Magnon dispersion for a square lattice antiferromagnet. The light gray dashed line indicates the magnetic Brillouin zone. (b) Transverse dynamical spin structure factor $S_{+-}(\omega)$ along the high symmetry lines of the Brillouin zone. The high symmetry points are $\Gamma = (0,0)$, $M = (\pi, 0)$ and $X = (\pi/2,\pi/2)$. (c) Two-magnon Raman spectrum $I(\omega)$ of a square lattice antiferromagnet. The blue lines show the parallel polarization component $I_{xx} = I_{yy}$, and the red lines show the cross polarization signal $I_{xy}$. The lightest lines are computed using a bare exchange value of $J_0 = 100$ meV, comparable to that of the parent cuprate La$_2$CuO$_4$. The modification from the cavity is taken to be $\Delta J = 2$ % or $\Delta J = 4$ %, corresponding to the darker lines and increasing in the direction of the arrow. The spectra are computed using an intrinsic Raman linewidth of $2$ meV.
• Figure 5: Photonic Density of States of a Fabry Perot cavity, measured at the center between the planar mirrors ($z = d / 2$). Shown are the in-plane (blue) and out-of-plane component, relative to their free space counterparts. The former density is relevant for the coupling to embedded 2D materials. Notice that the FP PDOS converges to the free space PDOS in the UV.