Surface Polaritons & Quantum-Geometric Coupling

• Surface polaritons and quantum-geometric coupling are hybrid modes at interfaces where light–matter interactions are modulated by quantum metrics and Berry curvature.
• The research highlights how interface geometry and material permittivities influence mode confinement, leading to enhanced light–matter coupling and distinct topological effects.
• These concepts underpin applications in tunable plasmonic devices, robust one-way channels, and momentum-resolved probes for quantum-enhanced photonic technologies.

Surface polaritons are hybrid light–matter modes confined to the interface between distinct media, most prominently metal–dielectric or polar dielectric–dielectric boundaries. Their electromagnetic fields decay exponentially away from the interface while propagating parallel to it. Quantum-geometric coupling refers to phenomena where the intrinsic band geometry—encoded via the quantum geometric tensor (QGT), comprising the quantum metric and Berry curvature—modulates the properties, responses, and interactions of surface polaritons. In recent years, the interplay between surface polariton modes and quantum geometry has been shown to underlie a broad class of physical effects in plasmonics, photonics, and condensed matter systems, ranging from enhanced light–matter coupling to topological photonic states.

1. Fundamental Theory of Surface Polaritons

Surface polaritons are collective excitations resulting from the coupling between electromagnetic waves and quasiparticles such as plasmons, phonons, or excitons at material interfaces. The canonical example is the surface plasmon polariton (SPP) at a metal–dielectric interface, with dispersion

$$k(\omega) = \frac{\omega}{c} \sqrt{ \frac{ \varepsilon_1(\omega)\varepsilon_2(\omega) }{ \varepsilon_1(\omega)+\varepsilon_2(\omega) } }$$

where $\varepsilon_{1,2}(\omega)$ are the frequency-dependent permittivities of the adjoining media. Extensions include surface phonon polaritons (SPhPs) in polar dielectrics and hybrid modes in layered nanostructures.

Quantum mechanical descriptions go beyond classical Maxwell boundary value problems, formulating SPPs as quantized bosonic modes. In the Power–Zienau–Woolley Hamiltonian, the bulk plasmon oscillators are nonperturbatively coupled to free-photonic continua, producing geometry-dependent renormalization of resonance frequencies and intrinsic ultrastrong light–matter coupling. The SPP dispersion emerges as an exact eigenmode in this framework, with surface-confined field profiles determined by the interface geometry and dielectric properties. In the quasistatic regime, even simple metal–dielectric interfaces support coupling strengths $g/\omega_p\sim0.1–0.3$, well within the ultrastrong-coupling domain, manifesting as nonzero ground-state plasmon/photon populations tunable by the curvature and refractive index (Maurer et al., 16 Jan 2026).

2. Quantum Geometric Tensor: Metric and Berry Curvature

The QGT provides a local, gauge-invariant characterization of the internal geometry of Bloch bands. For a given band $n$ at momentum $k$, its components

$T_{ij}(k) = g_{ij}(k) + \frac{i}{2} F_{ij}(k)$

combine the real symmetric quantum metric $g_{ij}(k)$ and the imaginary antisymmetric Berry curvature $F_{ij}(k)$. The quantum metric quantifies the overlap between nearby eigenstates and sets the “distance” in Hilbert space as a function of $k$. The Berry curvature, effectively a “magnetic field” in momentum space, underpins a range of geometric and topological effects.

Surface polariton bands in periodic metasurfaces—such as surface lattice resonances (SLRs) in a square array of plasmonic nanoparticles—acquire nontrivial QGT structure. For instance, in plasmonic lattices, band splitting and associated quantum metric enhancements originate from pseudospin–orbit coupling (polarization and propagation anisotropy), while nonzero Berry curvature arises solely due to non-Hermitian effects (loss-induced breaking of time-reversal symmetry) (Cuerda et al., 2023). The resulting $g_{ij}$ and $\varepsilon_{1,2}(\omega)$0 exhibit strong spatial localization in momentum space, such as peaks along Brillouin zone diagonals where band mixing is steepest.

3. Quantum-Geometric Coupling in Light–Matter Interactions

Quantum-geometric coupling refers to selection rules and transition amplitudes that depend explicitly on the quantum geometry of photonic, electronic, or polaritonic bands. In systems with nontrivial $\varepsilon_{1,2}(\omega)$1 or $\varepsilon_{1,2}(\omega)$2, even flat or nearly flat bands (with vanishing group velocity) remain optically addressable owing to their quantum metric. The interband Berry connection (matrix elements of the momentum derivative between bands) enables direct coupling to electromagnetic modes—particularly surface polaritons with finite in-plane momentum.

Under time-periodic drives (Floquet engineering), the effective Hamiltonian incorporates virtual processes mediated by the geometric structure of the bands. In sawtooth-chain flat band models, the coupling matrix element between bands is proportional to the difference in band energies and the interband Berry connection; thus, sideband transitions driven via a surface polariton can flatten or unflatten the band by quantum-geometric control. Surface polariton fields with finite $\varepsilon_{1,2}(\omega)$3 offer polarization and direction selectivity, allowing bond-specific renormalization of hopping parameters and hence tunable band geometry—far beyond what is attainable by free-space laser driving (Walicki et al., 2024).

4. Coherently Coupled Hybrid Quantum Systems

Surface polariton–quantum emitter hybridization realizes strong, geometry-dependent coupling regimes. At a metal–quantum-dot (QD) interface, the SPP mode coherently couples to localized QD excitons. The anticrossing (vacuum Rabi splitting) in the optical spectrum directly encodes the coupling strength $\varepsilon_{1,2}(\omega)$4, which depends on geometric factors such as QD size distribution, layer thickness, and dielectric environment. Adjusting these parameters enables selective control of SPP–exciton resonance and facilitates color-selective luminescence by tuning quantum-geometric properties (Bludov et al., 2011).

Analogously, phonon-polariton resonators and SPhPs in patterned SiC or piezoelectric superlattices support coherent coupling to localized excitonic or atomic transitions, with the collective coupling $\varepsilon_{1,2}(\omega)$5 reaching values far above all dissipation rates. In ensembles of Rydberg atoms placed near a PSL supporting SPhP modes, the ultra-large dipole moments and tight field confinement produce Rabi splittings $\varepsilon_{1,2}(\omega)$6MHz, enabling microwave-frequency optomechanical control at the single-quantum level (Sheng et al., 2016).

5. Topological and Spin-Hall Effects in Surface Polaritons

The quantum geometry of surface polaritons directly influences their topological and spintronic responses. All surface TM-polarized polaritons, irrespective of their origin (SPP, SPhP, loss–gain modes), exhibit spin–momentum locking: the local electric field carries a transverse spin that is strictly orthogonal to the propagation direction. The associated Berry curvature imparts a quantum spin Hall effect (QSHE) characterized by a quantized spin Hall coefficient $\varepsilon_{1,2}(\omega)$7 or $\varepsilon_{1,2}(\omega)$8, depending on the phase relationship and permittivity contrast at the interface (Xu et al., 2016). Transitions through parity–time (PT) symmetry boundaries induce topological phase transitions, flipping the sign of $\varepsilon_{1,2}(\omega)$9 and the accumulated Berry phase. Sign reversal in Im$g/\omega_p\sim0.1–0.3$0 across the interface can generate families of surface polaritons with damped oscillatory profiles and robust, quantized geometric characteristics absent in purely Hermitian, lossless systems.

6. Quantum-Geometric Photocurrents and “Polariton Drag”

The presence of quantum geometry in electronic bands (Berry curvature, quantum metric) can be interrogated via polariton-mediated optical processes. Polariton-drag photocurrents emerge when surface polaritons with finite wavevector $g/\omega_p\sim0.1–0.3$1 excite electronic transitions with momentum selectivity. In high-symmetry systems, such as bilayer graphene, polariton-drag can unblock otherwise symmetry-forbidden quantum-geometric photocurrent responses—most notably, injection and shift currents tied to the quantum metric and the shift vector, respectively (Xiong et al., 2021). The polariton’s large $g/\omega_p\sim0.1–0.3$2 and precise momentum selectivity enable polariton-selective photoexcitation (PSP), mapping out quantum-geometric quantities around the Fermi surface. This serves as a momentum-resolved probe of band geometry in materials where such effects are globally forbidden at $g/\omega_p\sim0.1–0.3$3.

7. Device Implications and Outlook

Quantum-geometric effects in surface polaritons yield a broad spectrum of potential applications. Finite quantum metric enables enhanced light–matter coupling for embedded emitters, nonclassical light generation via vacuum squeezing, and locally enhanced Purcell factors in engineered metasurfaces. Non-Hermitian Berry curvature induces anomalous group velocity corrections, facilitating direction-selective or chiral transport of polaritonic wavepackets controllable via material losses (Cuerda et al., 2023). Topologically robust one-way surface channels, spin-controlled switches, and nanoscale routing become accessible by leveraging spin–momentum locking and quantized Berry phases. Floquet engineering adds a further layer of tunability, enabling real-time control of band flatness, topological properties, and nonlinear responses in moiré materials and artificial lattices (Walicki et al., 2024). The intrinsically ultrastrong coupling regime discovered for even simple SPP structures suggests that quantum-geometric control of ground-state fluctuations—entanglement, squeezing, Casimir engineering—will be a pervasive and tunable resource in plasmonic and polaritonic quantum technologies (Maurer et al., 16 Jan 2026).