Nonlocal Light-Matter Interactions

• Nonlocal light-matter interactions are defined by spatially extended correlations in both fields and matter, leading to altered excitation rules and hybrid states.
• They utilize theoretical frameworks with momentum-dependent Hamiltonians and nonlocal dielectric responses to capture quantum and nanoscale phenomena.
• Experimental demonstrations in polar dielectrics, metamaterials, and 2D systems underscore applications like broadband Purcell enhancement and tunable quantum coupling.

Nonlocal light-matter interactions encompass the regimes where either the matter subsystem, the electromagnetic field, or both, exhibit spatial or spatiotemporal correlations beyond the scale at which the traditional local dipole approximation holds. This fundamentally modifies the nature, strength, and selection rules of excitation and emission processes, hybridizes photonic and material degrees of freedom, and enables emergent quantum phenomena with no analog in local response theory. Extensive research details nonlocal effects in polaritonic systems, condensed-matter models, nanometallic plasmonics, quantum optics, and engineered many-body photonic platforms.

1. Theoretical Framework: Spatial Dispersion, Nonlocal Dielectric Response, and Polaritonic Hybridization

The minimal quantum theory of light-matter interaction in nonlocal media employs coupled harmonic Hamiltonians with momentum-dependent (k-dependent) coupling and material response. In macroscopic quantum electrodynamics (MQED), the total Hamiltonian reads:

$$H = \sum_k \hbar\omega_k^\mathrm{ph}\,a_k^\dagger a_k + \sum_k \hbar\omega_k^\mathrm{m}\,b_k^\dagger b_k + \sum_k g_k(a_k + a_{-k}^\dagger)(b_{-k} + b_k^\dagger)$$

where %%%%1%%%% ($b_k$) are photonic (material) mode operators and $g_k$ is the wavevector-dependent (nonlocal) coupling strength (Rivera et al., 2020). The diagonalization yields polariton branches with admixtures of light and matter character. Nonlocality is introduced through k-dependent permittivity, e.g., in metals by the hydrodynamic Drude model:

$$\varepsilon_L(k, \omega) = 1 - \frac{\omega_p^2}{\omega(\omega + i\gamma) - \beta^2 k^2}$$

with $\beta^2 \sim (3/5)v_F^2$ (Fermi velocity) (Rivera et al., 2020, Luo et al., 2013). In polar crystals, optical phonon dispersion and spatial dispersion yield:

$$\varepsilon(k, \omega) = \varepsilon_\infty + \sum_j \frac{\omega_{P, j}^2}{\omega_{TO, j}^2 - \omega^2 - i\gamma_j\omega - \alpha_j k^2}$$

Nonlocal coupling breaks the standard equivalence between local field and polarization, requiring computation of emission and absorption rates via nonlocal Green’s functions or overlap integrals involving distributed wavefunctions and fields (Rivera et al., 2020, Kadochkin et al., 2017, Qian et al., 2021).

2. Nonlocal Phenomena in Polaritons, Thin Films, and Metamaterials

Nonlocality manifests strongly in nanoscale polar dielectrics, layered van der Waals structures, metamaterials, and metallic systems under high confinement. In mid-infrared polar dielectric thin films, the spatially dispersive optical phonon response yields hybrid longitudinal-transverse (LT) polaritons that strongly mix epsilon-near-zero (ENZ) and longitudinal optical (LO) phonon modes. The nonlocal constitutive relation,

$$D(\mathbf{r}, \omega) = \varepsilon_0\varepsilon_\infty E(\mathbf{r}, \omega) + P_{LO}(\mathbf{r}, \omega)$$

with $P_{LO}$ satisfying a hydrodynamic-like equation, leads to new eigenmodes whose dispersion and field profiles are governed by the slab thickness, nonlocal coupling parameter $\beta_L$, and optical phonon loss rate $\gamma$ (Gubbin et al., 2021). These LT hybrid modes enable energy transfer from LO currents to radiative ENZ components, relevant for energy-funneling mid-IR emitters.

In plasmonic and hyperbolic metamaterials, nonlocality is engineered via nanorod assemblies or designed composites. Nonlocal effective medium theory for a uniaxial nanorod array modifies the $zz$-component of the permittivity to

$$\varepsilon_{zz}(k_z, \omega) = \varepsilon_h + \frac{p (\varepsilon_m - \varepsilon_h)}{1 - \frac{k_z^2 c^2}{\omega^2}\frac{\varepsilon_m - \varepsilon_h}{\varepsilon_h}}$$

resulting in multiple TM modes and a boosted local density of photonic states (LDOS), especially in the elliptic (non-hyperbolic) regime—an effect directly measured as broadband Purcell enhancement of emission (Ginzburg et al., 2016).

For nanoplasmonic and sub-nm gap systems, the Thomas–Fermi hydrodynamic model predicts a spatial “smearing” of induced charge over the Thomas–Fermi screening length, leading to finite wavevector cutoffs in surface-plasmon polariton (SPP) dispersion and strict limitations on field confinement (LAM: thin dielectric cover model) (Luo et al., 2013). These corrections set fundamental bounds on field enhancement in nonlinear and sensing applications.

3. Quantum Emitter, Exciton-Photon, and Many-Body Extensions

When quantum emitters or collective excitations are sufficiently delocalized or have large spatial extent, the local-dipole approximation for light–matter coupling $$g_\mathrm{local} \propto \mathbf{d} \cdot \mathbf{E}(r_0)$$ is invalid. In 2D transition-metal dichalcogenides (TMDs) and encapsulated monolayer MoS$_2$, excitons and trions exhibit center-of-mass (COM) wavefunctions spreading over hundreds of nanometers. The relevant coupling is then

$$g_\mathrm{nonlocal} \propto \int \Psi_{COM}(r)\,E_{cav}(r)\,d^3r$$

where $E_{cav}(r)$ is the cavity mode profile (Qian et al., 2021). Temperature-tunable COM diffusion enhances or suppresses light-matter coupling strength in high-Q nanocavities, leading to nonmonotonic temperature dependence consistent with nonlocal coupling theory.

In many-body photonic systems, e.g., dye-filled microcavities, nonlocal photon–photon interactions arise from thermally mediated refractive index changes with a diffusion kernel $G(r-r')$. The result is a generalized Gross–Pitaevskii equation with a nonlocal nonlinear potential:

$$\mu\,\psi(r) = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(r) + gN_0 \int d^2r' K(r - r') |\psi(r')|^2 \right]\psi(r)$$

This structure enables surface localization, modulation instability, and collective behavior not accessible in local-contact interacting Bose gases (Strinati et al., 2021, Shahmoon et al., 2014).

4. Ultrafast and Quantum Effects: Dynamical Casimir Emission, Coherent Delocalization, and Entanglement

Temporal modulation of nonlocal, dispersive permittivities yields qualitatively new facets in quantum emission, notably in the context of the dynamical Casimir effect. In time-varying dispersive nanophotonic systems, nonlocality regularizes divergences present in models that neglect spatial dispersion, with the emission spectrum and rate of polariton pairs converging only when the asymptotic $q \rightarrow \infty$ response includes the spatial cutoff scale (Gangaraj et al., 2024). Specifically, the nonlocal Lorentzian oscillator for optical phonons introduces a $q^{-11}$ decay in the emission integrand, eliminating the unphysical divergence and predicting measurable spectral broadening.

Coherent delocalization of the center of mass wavefunction of particles leads to nonlocal emission and absorption probabilities, with first-principles calculations based on the generalized Unruh-deWitt model. A key prediction is that sufficiently rapid coherent spreading can induce “virtual” Cherenkov-like emission, even for neutral systems, whenever components of the wave packet exceed the relevant phase velocity in a medium (Stritzelberger et al., 2019).

Entangled light-matter interactions introduce another nonlocal dimension: in two-photon absorption mediated by entangled photon pairs, the absorption cross-section becomes linear in the pair flux (not quadratic), and the rates depend on the joint spectral amplitude of the biphoton state rather than just the one- or two-photon DOS. The underlying transition amplitude integrates material and field degrees of freedom nonlocally in joint time-frequency space, generating fundamentally new scaling, selection rules, and opportunities for materials control in quantum-enabled spectroscopies (Szoke et al., 2020).

5. Experimental Manifestations and Methods: Bypassing, Probing, and Modeling Nonlocality

Experimental access to nonlocal regimes leverages advanced nanofabrication, cavity-QED, near-field microscopy, and numerical modeling. In hBN/Au/air heterostructures, phonon-polaritons can be confined to effective indices exceeding 90, even as their phase velocity closely approaches the Fermi velocity of the screening metal, yet experimental near-field imaging and interface-sensitive characterization reveal that a sub-nm interfacial dielectric layer can “bypass” the onset of significant nonlocal correction—the energy remains largely in the dielectric, and nonlocal corrections in gold (<1% for $t_{\mathrm{hBN}} \gtrsim 10$ nm) are negligible (Heiden et al., 21 Mar 2025). This identifies phonon-polariton systems as platforms to reach high confinement unconstrained by metallic nonlocality, unlike graphene acoustic plasmons.

The granular-permittivity model enables semi-classical simulation of nonlocal light–matter interaction by discretizing the near-interface zone into polarizable spheres matched to the bulk permittivity. This reproduces far-field optical properties while accurately capturing local-field quenching effects at separations down to sub-nm scales—a regime where ab initio models are computationally infeasible (Kadochkin et al., 2017).

The “local-analogue model” (LAM) recasts hydrodynamic nonlocal response at surfaces into an equivalent local multilayer with a thin dielectric spacer of appropriate permittivity and thickness, quantitatively capturing reflection, transmission, and near-field enhancement, and providing a practical simulation and design tool for atomic-scale plasmonic devices (Luo et al., 2013).

6. Applications, Engineering, and Future Directions

Nonlocal light-matter interactions underlie diverse phenomena: LT-polariton-induced energy funneling in polar dielectrics (Gubbin et al., 2021), broadband Purcell enhancement in engineered metamaterials (Ginzburg et al., 2016), tunable strong and ultrastrong coupling in 2D material–cavity systems (Qian et al., 2021), collective photon condensate self-ordering (Strinati et al., 2021), nonlocal nonlinear optics and photonic quantum simulations (Shahmoon et al., 2014), and precision quantum metrology via entangled-photon spectroscopies (Szoke et al., 2020).

The extension of MQED and nonlocal response theory to topological, moiré, and strongly correlated photonic systems is ongoing (Rivera et al., 2020). Integrated, chip-scale manipulation of entangled-light–matter interactions, on-demand control of emission pathways via spatial engineering of fields and materials, and advanced quantum simulation paradigms leveraging nonlocal photon–photon and photon–matter couplings represent active frontiers. Crucially, engineered nonlocality is a new degree of freedom in nanophotonics, opening possibilities for broadband quantum emitters, quantum nonlinear optics, ultrafast frequency conversion, and robust quantum interfaces not possible in the local-response paradigm.