Nanophotonics for pair production

The study addresses how to efficiently produce electron-positron pairs from light, a fundamental prediction of relativistic QED. Classical mechanisms include Breit–Wheeler (BW) photon–photon scattering, Bethe–Heitler (BH) production in the Coulomb field of nuclei, and Landau–Lifshitz (LL) processes mediated by virtual photons. While pair production has been realized via energetic electrons and laser photons or via real photons from atomic collisions, cross sections remain exceedingly small, limiting practical positron sources which currently rely on beta decay, moderation, and trapping. The authors propose leveraging strongly confined optical near fields (polaritons) supported by nanostructures to enhance the pair-production probability when combined with γ-ray photons. Surface and gap polaritons in 2D and nanostructured materials offer large field confinement and momentum, potentially alleviating kinematic mismatch and enabling pair creation with near-threshold γ-photons, opening the way to ultrafast and nanoscale positron sources.

The paper situates its contribution within foundational pair-production mechanisms: BW (two real photons), BH (photon–nucleus interaction), and LL (two virtual photons). Prior experimental realizations involved multiphoton light-by-light scattering and real-photon collisions. Applications of positrons span surface science (PAS, LEPD), antimatter formation (antihydrogen, positronium), and beam technologies relying on beta decay and trapping. On the photonics side, extensive progress in nanophotonics and 2D materials has established long-lived, strongly confined plasmonic, phononic, and excitonic polaritons from mid-IR to visible frequencies, including extreme field enhancements in nanogaps and plasmonic hotspots (e.g., SERS). These advances motivate using confined optical modes to increase pair-production rates by breaking translational invariance and supplying high in-plane momentum, unlike free-space photons that suffer strong kinematic mismatch in BW at optical energies (which would otherwise require GeV–TeV partner photons, as encountered in astrophysical contexts).

The authors develop a quantum electrodynamics framework using the relativistic minimal coupling Hamiltonian H(t) = ∫ d^3r j(r)·A(r,t), where j(r) = ec Ψ̄(r)γΨ(r) is the fermionic current and A is the classical vector potential containing both the γ-ray and polariton fields in a gauge with vanishing scalar potential. The fermionic field operator is expanded in plane-wave electron and positron spinor modes. The electromagnetic field comprises a monochromatic γ-ray plane wave propagating along z with polarization e_j and a spatially localized polaritonic field E_p(r) oscillating at ω_p. Pair-production rates into electron–positron states |d_q,s^† a_q',s'^†⟩ are calculated to second order in time-dependent perturbation theory, adequate given the low cross sections, with possible nonperturbative corrections noted via renormalization group methods. The resulting positron-momentum-resolved cross section per incident γ-photon and per polariton involves spin-summed squared matrix elements built from Dirac γ matrices and the Feynman propagator G_F, and the momentum-space Fourier components of the polariton field E_p(k). The analysis treats two geometries: (1) Surface polaritons on a 2D material (z=0), modeled with an evanescent field having in-plane wavevector k_p and exponential decay away from the surface, neglecting losses and finite thickness, leading to parallel momentum conservation q_∥ = k_p, energy conservation E_q = ω_γ − ω_p, and constraints on q_z. The polariton’s out-of-plane momentum distribution enters via its Fourier transform, producing an analytic differential cross section dσ^pol/d^3q. (2) Gap polaritons: a deeply confined mode in a vacuum gap, approximated as a uniform field inside a sphere of radius R_p with amplitude E_0 and frequency ω_p. Inserting the normalized Fourier transform of this confined mode into the general expression yields an analytic differential cross section versus emission angle. Numerical evaluation integrates over momenta/angles to obtain total cross sections and emission angular distributions. Throughout, results are compared to BW photon–photon cross sections and to BH cross sections per atom for relevant materials (graphene, gold), normalizing appropriately per polariton and per atom to assess detectability against background. Practical estimates incorporate realistic laser-driven polariton populations using field enhancements (~10^2), ultrafast pulse amplitudes (~10^9 V/m), and mode volumes consistent with nanogap geometries.

• Polaritonic assistance dramatically relaxes the kinematic constraints of free-space BW scattering: with confined polaritons, near-threshold γ-photons (≈1.02–1.17 MeV, e.g., 60Co at 1.17 MeV) can produce pairs with eV-scale polaritons, whereas BW with an optical photon would require ≳0.1 TeV partner photons.
• Calculations show the total polariton-assisted cross section σ^pol (integrated over fermion momenta) exceeds the BW cross section by several orders of magnitude across a wide γ-energy range up to TeV, attributable in part to spatial compression and broken translational invariance of polaritons.
• Emission kinematics: positron emission is strongly forward-peaked along the γ-ray direction and dominated by approximately equal kinetic energy sharing between electron and positron for both near-threshold and GeV energies.
• Surface polaritons vs BH background: For 1.17 MeV γ-photons interacting with a highly doped graphene monolayer supporting ~1 eV plasmons, σ^pol per polariton ≈ 10^−1 barn, while σ^BH per carbon atom ≈ 10^−4 barn. Given the carbon surface density (≈40 nm^−2), reaching comparable yields would require unrealistically high plasmon densities (~10^10 nm^−2), implying BH dominates in planar geometries.
• Gap polaritons provide strong enhancement and background suppression: Deep 3D confinement boosts σ^pol per polariton by several orders compared to surface modes, and emission originates in the vacuum gap where BH does not occur. For a representative gold gap mode with ħω_p = 0.1 eV, R_p = 50 nm, field enhancement ~10^2 (E_p ≈ 10^10 V/m), and ultrafast laser peak field 10^9 V/m, the number of polaritons per gap is N_p ≈ 3×10^7. Using σ^pol ≈ 0.25 barn per polariton, the positron yield fraction per γ-photon is ≈ η×10^−7, where η is the fractional surface coverage by gaps.
• BH comparison for gold film: For a 100 nm Au film, σ^BH per Au atom at 1.17 MeV ≈ 16 mbarn and atomic volume ≈17 Å^3 yield a surface atom density ≈6×10^3 nm^−2 and an estimated BH positron fraction ≈10^−8 per incident γ-photon. Thus, the ratio of polariton-assisted to BH emission is ≈10η; for η ≈ 0.1, the two signals are comparable.
• Practical yield estimate: With 1 g of 60Co and 1 ps laser pulses, ≈100 γ-photons overlap temporally with each pulse, producing ~10^2 positrons per pulse, roughly half from polariton-assisted scattering, at high repetition rates (~10^9 Hz), indicating measurable signals.

The work demonstrates that using confined polaritonic near fields with γ-rays addresses the core challenge of BW pair production—kinematic mismatch—by breaking translational invariance and supplying large in-plane momentum, thereby enabling pair creation with near-threshold γ-photons. Spatial confinement enhances coupling to high-momentum fermionic final states, producing cross sections far exceeding free-space BW. However, in planar structures the signal is typically obscured by BH background from the material. The proposed use of gap polaritons confines the optical mode to a vacuum region, eliminating BH generation there and increasing the polariton-assisted cross section through full 3D confinement. Synchronizing detection with ultrafast laser pulses that excite high polariton populations further improves the signal-to-background ratio. The predicted forward-peaked, ultrafast, nanoscale positron emission is relevant for compact positron sources, potentially enabling temporal and spatial beam shaping via control of the polaritonic field distribution and polarization. The approach also suggests exploring the inverse process—polaritonic-field-assisted positron annihilation—as a route to localized γ-photon sources.

The paper introduces a nanophotonics-based mechanism for generating electron–positron pairs by combining γ-rays with strongly confined polaritonic fields. This approach substantially enhances pair-production cross sections relative to free-space BW scattering and lowers the requisite photon energies to near-threshold γ-rays. Although BH scattering dominates in planar materials, employing gap polaritons achieves both strong enhancement and spatial discrimination, enabling detectable polariton-assisted signals under ultrafast pulsed excitation. The work opens opportunities for ultrafast, nanoscale positron sources with tailored spatiotemporal properties, beam shaping (e.g., chiral or multi-pulse positron states), and potential localized γ-photon generation via the inverse process. Future research directions include experimental realization with gap/nanoparticle plasmons, optimization of nanostructure geometries and materials, improved γ-ray focusing and alignment, development of positron microscopy for selective collection, and exploration of nonperturbative effects and loss/dispersion in realistic materials.

• In planar (surface polariton) geometries, the polariton-assisted signal is orders of magnitude smaller than BH background from the material, complicating detection.
• Some estimates rely on idealized field models (lossless media, uniform spherical modes), neglecting material losses, screening, and finite-thickness effects; real structures may modify yields.
• Calculations use second-order perturbation theory; nonperturbative corrections are not included and could affect quantitative results at higher intensities.
• The approach requires synchronization with ultrafast laser pulses to achieve high polariton populations; timing jitter and practical repetition rates impact yields.
• Focusing γ-rays onto nanoscale regions is challenging and may limit practical implementation.
• Achieving extremely high polariton densities to compete with BH in planar systems is unrealistic, motivating reliance on gap/nanoparticle confinement and selective detection.