Nanophotonics for pair production

The transformation of electromagnetic energy into matter, specifically electron-positron pair production from light, is a fascinating prediction of relativistic quantum electrodynamics. While theoretically possible, the probability of this phenomenon is extremely low. Current positron sources rely on beta decay, necessitating complex monochromatization and trapping techniques to produce high-quality beams. This paper explores an alternative approach: leveraging the intense, confined optical near fields of nanostructured materials to enhance pair production. The core hypothesis is that the interaction between near-threshold gamma rays and surface polaritons—hybrids of light and polarization charges—will significantly increase the pair-production cross section compared to free-space photon interactions. This approach is motivated by the short in-plane wavelengths and strong field confinement exhibited by surface polaritons, potentially mitigating the kinematic mismatch inherent in the Breit-Wheeler (BW) pair production process. Successful demonstration of this method would represent a significant advancement, bridging the gap between particle physics and nanophotonics and enabling the creation of tunable pulsed positron beams from nanoscale regions. The resulting source would offer unique advantages over traditional beta-decay-based methods, potentially leading to advancements in various fields including surface science, antimatter studies, and other applications requiring high-quality positron beams.

The theoretical basis for pair production was established in 1934 through the independent work of Breit and Wheeler (BW) describing photon-photon scattering, Bethe and Heitler (BH) detailing photon-nucleus interactions, and Landau and Lifshitz (LL) focusing on particle-particle collisions. These processes differ in the nature of photons involved: real photons for BW, virtual photons for LL, and a combination of both for BH. Experimental realization has historically involved high-energy electron-photon collisions or more recently, solely real photons from atomic collisions. The generation of positrons is vital in numerous applications including positron annihilation spectroscopy, low-energy positron diffraction, and the creation of antimatter such as antihydrogen and positronium. Current methods typically involve beta decay followed by deceleration and trapping to obtain slow, monochromatic positron pulses. Direct positron generation from light, while highly desirable, has been hindered by extremely low cross-sections. This paper addresses the need for novel methods to enhance pair production rates by focusing on the interaction between confined optical modes and high-energy photons, building upon recent advancements in nanophotonics and the utilization of surface polaritons in various applications.

The authors employ relativistic quantum electrodynamics to calculate the pair-production cross section. They begin by considering a general configuration involving the interaction of a gamma-photon (γ-photon) and a confined polariton supported by a nanostructured material. The theoretical framework utilizes the relativistic minimal coupling Hamiltonian, which incorporates the fermionic current and the classical vector potential associated with both the polariton and photon fields. The vector potential is expressed as the sum of two monochromatic components representing the polariton and γ-photon fields, respectively. The polariton electric field is described using expressions derived from models of surface modes in planar surfaces and nanostructures. These models have previously shown success in explaining experimental results in nanophotonics. The pair-production rate for a state comprising an electron and a positron is calculated to the lowest non-vanishing order of time-dependent perturbation theory. The calculation considers both polariton emission and absorption processes. The momentum-resolved pair-production cross-section is derived, taking into account the spatial confinement and wave-vector distribution of the polariton field. The authors investigate two illustrative scenarios: surface polaritons excited on a 2D material and gap polaritons confined within a three-dimensional structure. For surface polaritons, they derive an expression for the cross-section incorporating the in-plane momentum conservation and energy conservation conditions. For gap polaritons, they simplify the field model to a uniform field within a spherical region to derive analytical expressions. The calculated cross-sections are then compared with those of the Bethe-Heitler (BH) scattering process, which represents a dominant background signal in materials supporting polaritons. The comparison accounts for material properties and polariton density, to assess the feasibility of detecting the polariton-assisted pair production signal above the background noise. Detailed derivations and calculations are provided in supplementary notes.

The key findings highlight a substantial enhancement of pair production cross sections when near-threshold γ-photons interact with confined polaritons, compared to free-space BW scattering. This enhancement arises from the spatial confinement of surface polaritons, which allows pair production at γ-photon energies just above the 2mc² threshold. This contrasts with free-space BW scattering, requiring much higher photon energies. The calculated cross-sections reveal a significant increase in pair production when using low-energy polaritons (a few eV) and near-threshold γ-photons (around 1.17 MeV). The momentum-integrated cross-section for polariton-assisted pair production is several orders of magnitude higher than the BW cross section at γ-photon energies up to the TeV regime. However, this polariton-mediated production remains significantly smaller than the BH scattering contribution in the case of surface polaritons. This is mitigated by using gap polaritons confined to vacuum regions flanked by a polaritonic material. The suppression of the BH background in gap structures, and the resulting increased signal, makes it more realistic to detect pair production mediated by gap plasmons. In a numerical example using gold gaps of 50 nm and a 1.17 MeV γ-photon, the authors demonstrate that the polariton-assisted pair production becomes comparable in magnitude to the BH scattering when synchronizing the positron detection with the laser pulses exciting the polaritons, highlighting the importance of ultrafast, synchronized detection. The proposed method allows for the generation of ultrafast positron pulses with nanoscale spatial confinement, offering advantages over traditional positron sources. The angular distribution of positron emission is examined, showing a sharp peak around the forward direction of the γ-ray.

The findings address the research question by demonstrating the feasibility of significantly enhancing electron-positron pair production using nanostructured materials and confined optical modes. The enhancement arises from overcoming the kinematic mismatch inherent in the BW process through the short wavelengths and strong field confinement of surface polaritons. Although BH scattering is typically a dominant background signal, the authors show that this can be mitigated by employing gap polaritons and synchronized detection with ultrafast laser pulses. The results highlight the potential of this nanophotonic approach to pair production, offering new capabilities in the generation of tunable, ultrafast positron pulses from nanoscale sources. The proposed method opens up exciting possibilities for studying fundamental physics at the nanoscale and has potential applications in various fields.

This study proposes and theoretically validates a novel method for significantly enhancing electron-positron pair production using the interaction of near-threshold γ-photons and confined polaritons. The spatial confinement of polaritons in both surface and gap geometries is crucial in overcoming the energy-momentum mismatch. While BH scattering presents a background signal, the use of gap polaritons and synchronized detection schemes greatly enhances the visibility of the proposed mechanism. Future research should focus on experimental verification of the theoretical predictions, further optimization of the nanostructures, and exploring different materials and polariton modes to maximize the pair-production efficiency. Applications such as the generation of chiral positron beams, ultrafast positron pulses, and spatially confined positron sources are also areas for future investigations.

The study is primarily theoretical, relying on numerical calculations and simplified models of polariton fields and materials. Experimental verification is essential to confirm the theoretical predictions. The analysis focuses on specific nanostructures (gaps and surface polaritons), and further investigation might be needed to explore the effectiveness of other geometries. The comparison with BH scattering assumes certain material properties and conditions, which may vary depending on the experimental setup. The authors acknowledge the challenge of focusing γ-photons precisely onto the region of high polariton intensity. The detection scheme relies on synchronization with ultrafast laser pulses, requiring advanced experimental techniques.