Nanophotonics for pair production

Article https://doi.org/10.1038/s41467-023-43701-5 Nanophotonics for pair production Received: 21 August 2023 Valerio Di Giulio 1 & F. Javier García de Abajo 1,2 Accepted: 9 November 2023 1234567890():,; 1234567890():,; Check for updates The transformation of electromagnetic energy into matter represents a fascinating prediction of relativistic quantum electrodynamics that is paradigmatically exemplified by the creation of electron-positron pairs out of light. However, this phenomenon has a very low probability, so positron sources rely instead on beta decay, which demands elaborate monochromatization and trapping schemes to achieve high-quality beams. Here, we propose to use intense, strongly confined optical near fields supported by a nanostructured material in combination with high-energy photons to create electron-positron pairs. Specifically, we show that the interaction between near-threshold γ-rays and polaritons yields higher pair-production cross sections, largely exceeding those associated with free-space photons. Our work opens an unexplored avenue toward generating tunable pulsed positrons from nanoscale regions at the intersection between particle physics and nanophotonics. The creation of massive particles from electromagnetic energy emerged as a prominent focus of attention in 1934, when the materialization of an electron and its antiparticle—the positron—was predicted to occur with nonvanishing probability by Breit and Wheeler (BW) from the scattering of two photons1, by Bethe and Heitler (BH) from the interaction of a photon and the Coulomb potential of a nucleus2, and by Landau and Lifshitz (LL) from the collision of two other massive particles3. A main difference between these processes relates to the real or virtual nature of the involved photons. While only real electromagnetic quanta lying inside the light cone (i.e., satisfying the light dispersion relation in vacuum, k = ω/c) participate in the BW mechanism for pair production, the LL process is mediated by two virtual photons, and both real and virtual photons play a role in BH scattering. Eventually, pair production was achieved by colliding energetic electrons and real photons delivered by high-power lasers4, and more recently using only real photons generated from atomic collisions5. Besides the fundamental interest of these processes, the generation of positrons finds application in surface science6 through, for example, positron annihilation spectroscopy7–9 and low-energy positron diffraction10, as well as in the study of their interactions with atoms and molecules11,12. Positrons are also used to create antimatter, for example, antihydrogen13–16 and positronium17. In these studies, slow positrons are commonly obtained from beta decay, decelerated through metallic moderators18, and subsequently stored in different types of traps, from which they are extracted as low-energy, quasimonochromatic pulses19–22. Direct positron generation from light would not require nuclear decay and could further leverage recent advances in optics to produce ultrashort photon pulses. However, the cross-sections associated with the aforementioned processes are extremely small. As a possible avenue to increase the pair-production rate, we consider the replacement of free photons by confined optical modes in the hope that they alleviate the kinematic mismatch between the particles involved in BW scattering. In particular, surface polaritons, which are hybrids of light and polarization charges bound to material interfaces, can display short in-plane wavelengths compared with the freespace light wavelength. Such modes involve electromagnetic energy trapped at the interface between two media with different dielectric properties. For example, for a planar interface, when the sign of the real part of the permittivity of the two media is opposite, the associated optical fields decay exponentially away from the interface, but a similar behavior is observed when light is trapped by a thin metallic film23. Likewise, light can be trapped in polaritons sustained by more involved geometries24 (e.g., in a self-standing sphere, a polariton is defined by the condition that its permittivity is equal to −2 if one neglects retardation effects). Actually, a broad suite of twodimensional (2D) materials has recently been identified to sustain including long-lived, strongly confined polaritons25,26, 23,27,28 29,30 , phononic , and excitonic31 modes that cover a plasmonic wide spectral range extending from mid-infrared frequencies23,27,29,30 to the visible domain28,31. Specifically, modes bound to nanogaps32 feature large field confinement and enhancement (in vacuum 1 ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain. 2ICREA-Institució Catalana e-mail: de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain. Nature Communications | (2023)14:8189 1 Article https://doi.org/10.1038/s41467-023-43701-5 regions) that boost light-mediated processes, such as surfaceenhanced Raman scattering (SERS). In this work, we calculate the pair-production cross section associated with the annihilation of γ-ray photons (γ-photons) and confined polaritons, leading to a substantial enhancement compared to free-space BW scattering. Part of this enhancement relates to the spatial confinement of surface polaritons, as the lack of translational invariance enables pair production for γ-photon energies just above the 2mec2 threshold (e.g., at the 60Co emission line ℏωγ ~1.17 MeV combined with a polariton energy ℏωp of a few eV), in contrast to freespace BW scattering, for which visible-range photons need to be paired with GeV photons such as those generated in astrophysical processes33,34. The latter include absorption of high-energy γ rays by extra-galactic background light35, by active galactic nuclei36, and during γ-ray bursts37, as well as plasma production in neutron-star magnetospheres38. For polaritonic nanogap modes confined in three dimensions, pairs can be produced by γ-photon scattering in the gap vacuum region, where polariton-mediated positron emission is not affected by the background of other emission processes such as BH scattering. By demonstrating the advantages of using deeply confined light, our work inaugurates an avenue in the exploration of nanophotonic structures as a platform for high-energy physics. Results Pair production from the scattering of a polariton and a γphoton Considering the general configuration illustrated in Fig. 1a, we study pair production by using the relativistic minimal coupling Hamiltonian39,40 ^ int ðtÞ = 1 H c Z 3 d r ^jðrÞ  Aðr, tÞ, ð1Þ !^ : is the fermionic current, A(r, t) is the where ^jðrÞ =  ec : ΨðrÞ γ ΨðrÞ classical vector potential associated with the polariton and photon fields, and we adopt a gauge with vanishing scalar potential. Here, : ⋅ : denotes normal product concerning electron and posit (...truncated)