Phase-locked photon-electron interaction without a laser

The study addresses how to achieve strong, phase-locked mutual coherence between photons and electrons inside an electron microscope without relying on external ultrafast lasers and complex synchronization. Conventional ultrafast electron microscopy uses laser-driven photoemission to generate pulsed electrons and a second synchronized laser to excite the sample, which imposes technical complexity and limits mutual coherence. The authors propose an inverse approach: use the electron beam itself to generate a compact internal electron-driven photon source (EDPHS) that emits photons phase-locked to the electron’s near field. By enabling controlled, delay-tunable, mutually coherent photon–electron interactions, the work aims to retrieve spectral phases and perform spectral interferometry, facilitating coherent control and correlation spectroscopy of excitations such as exciton-polaritons in quantum materials.

Prior work in ultrafast electron microscopy has visualized ultrafast dynamics in materials, including plasmons and phonon polaritons, and established photon-induced near-field electron microscopy (PINEM) as a means to study photon–electron interactions and tailor quantum-path interferences of single-electron wavepackets. Conventional approaches require extrinsic ultrafast laser excitation and careful synchronization. Electron-beam spectroscopies, including cathodoluminescence (CL) and electron energy-loss spectroscopy, have probed exciton–photon/plasmon coupling and polaritons in 2D semiconductors. Strong exciton–photon coupling in thin transition metal dichalcogenide (TMD) flakes (e.g., WSe2) produces lower- and upper-polariton branches, observable in CL. Spectral interferometry is a standard laser-based tool to recover amplitude and phase but is typically limited to paraxial detection. The literature lacks a compact, laser-free method to generate a mutually coherent optical reference inside an electron microscope and to retrieve spectral phase across momentum space; the present study fills this gap using an electron-driven photon source (EDPHS).

• Concept and setup: An electron beam (30 keV) sequentially interacts with (1) a nanostructured electron-driven photon source (EDPHS) and then (2) the sample. The EDPHS emits a collimated, broadband, TM-polarized photon beam phase-locked to the exciting electron. The emitted photons and the electron-induced sample radiation are detected via angle-resolved cathodoluminescence (CL), enabling momentum–energy-resolved interferometry.
• EDPHS design: Array of nanopin-holes in a 40 nm Au film on a Si3N4 membrane (focused-ion-beam milled). Hole radii gradually vary from 25 nm (inner rim) to 150 nm (outer rim), supporting broadband emission. Electron-induced surface plasmon polaritons in the EDPHS scatter off the holes and radiate to the far field as a Gaussian beam.
• Delay control: Due to v≠c, the relative delay τ between EDPHS photons and electrons at the sample is set by the distance L: τ = L(v⁻¹ − c⁻¹). For 30 keV electrons, v ≈ 0.328c, giving 6.8 fs per 1 nm change in L. Piezo stages (six degrees of freedom, independent motion of EDPHS and sample) allow tuning τ from ~0 to ~40.8 ps (L up to 6 mm).
• Samples: Exfoliated WSe2 flakes (≈80 nm thick) on holey carbon TEM grids. WSe2 hosts A and B excitons at ~1.68 eV (738 nm) and ~2.05 eV (604 nm). Strong exciton–photon coupling yields LP and UP branches.
• CL measurements: SEM (Zeiss SIGMA, 30 kV, 1–14 nA) with Delmic CL detector and an off-axis Al-coated parabolic mirror (acceptance 1.49 sr). CCD-based spectral detection. Angle-resolved maps acquired with 50 nm spot, typical 10 s per step; energy–momentum maps via one-dimensional slit and grating (integration ~150 s). Spectral filtering examples: λ = 800 ± 10 nm; angular filtering examples: θ = 45° ± 2°, φ = 100° ± 2° (k∥ ≈ 0.707k0). CL spectra acquired for EDPHS alone, sample alone, and combined, over varying L.
• Data products: Three-dimensional data cubes (CL intensity vs. kx, ky, λ) as a function of L (hence τ). Additional L–k interferograms constructed by scanning L and recording CL vs. transverse momentum.
• Interferometric model: The total momentum-resolved CL spectrum Γc(k,ω) is expressed as the incoherent intensities of EDPHS and electron-induced fields plus cross-terms that depend on τ, yielding interference fringes in energy and momentum spaces. For fixed k, ΓCL(ω) decomposes into a τ-independent term Γ0 and two τ-dependent terms Γ± ∝ e±iωτ. Fourier transforming ΓCL(ω) to time identifies peaks at t = 0 (d.c.) and t = ±τ (a.c.). The degree of mutual coherence is quantified as the a.c./d.c. ratio under comparable intensities. A phase-retrieval algorithm isolates Γ+ to retrieve the relative spectral phase and amplitude σ(ω) = Ez,sample/Ez,EDPHS.
• Numerical simulations: FDTD simulations generate EDPHS radiation and electron-induced fields in and around a rectangular WSe2 flake. Superposition at controlled delays is propagated to the far field via Green’s functions to obtain simulated momentum–distance interference maps.
• Analytical path model: Four optical pathways are considered: (1) direct transmission of EDPHS radiation through the flake, (2) EDPHS radiation scattered from the flake edge(s), (3) transition radiation from the electron crossing the flake, and (4) exciton–polaritons directly excited by the electron and their edge scattering. Interference among these paths explains the observed L–k interference patterns. EDPHS radiation does not directly excite EPs due to momentum mismatch; edge scattering mediates coupling.
• Calibration and controls: CL spectra of EDPHS-only and sample-only are used to balance intensities for coherence estimates. Delay verification via τ = L(v⁻¹−c⁻¹) consistency (e.g., L = 20, 22, 30 µm give t ≈ ±136, ±150, ±204 fs peaks after Fourier transform).

• Demonstration of internal, phase-locked photon–electron interaction: An electron-driven photon source (EDPHS) inside the SEM generates photons mutually coherent with the electron’s near field, enabling interferometry without an external ultrafast laser.
• Measured mutual coherence: Degree of mutual coherence of approximately 27%, inferred from the ratio of a.c. to d.c. components in Fourier-transformed CL spectra and supported by agreement between experiment and classical electromagnetic simulations.
• Delay-tunable interference: Clear interference fringes observed in both momentum and energy domains as a function of the EDPHS–sample distance L (delay τ). Coherent interference region spans roughly L ≈ 22–40 µm; visibility diminishes for L > 40 µm due to decoherence.
• Spectral interferometry with continuous electron beams: Retrieval of the relative spectral amplitude and phase σ(ω) = Ez,sample/Ez,EDPHS from CL data via Fourier-domain separation of a.c./d.c. terms, demonstrating spectral interferometry in an electron microscope.
• Temporal metrics: Fourier-domain d.c. peak full width at half maximum ≈ 5.2 fs, indicating temporal broadening of EDPHS and sample radiation of ~5.2 fs. Example delay peaks: t = ±136 fs (L = 20 µm), ±150 fs (L = 22 µm), ±204 fs (L = 30 µm), consistent with τ = L(v⁻¹ − c⁻¹) for 30 keV electrons (v ≈ 0.328c). Delay tunability is 6.8 fs per 1 nm change in L; dynamic delay range up to ~40.8 ps.
• Mode selectivity and dispersion: EDPHS emission (peaked near 800 nm) efficiently excites the lower-polariton branch in WSe2; combined CL spectra and momentum-resolved maps reveal LP/UP features and their momentum-dependent blueshift, consistent with EP dispersion.
• Model and simulation validation: FDTD simulations and a four-path analytical model reproduce measured L–k interferograms and spectral interferences, attributing patterns to interference among direct EDPHS transmission, edge-scattered EDPHS light, electron transition radiation, and EP excitation plus edge scattering.
• Accuracy and robustness: Phase retrieval is consistent for L = 20 and 22 µm; up to ~20% phase variation observed when comparing L = 20 vs. 30 µm, setting an accuracy estimate tied to fringe visibility.

By generating the optical reference internally via an electron-driven photon source, the study circumvents the need for synchronized ultrafast lasers and complex timing schemes in ultrafast electron microscopy. The mutual coherence between EDPHS photons and electron-induced sample radiation is sufficient (≈27%) to perform spectral interferometry, enabling retrieval of relative spectral phase and amplitude across momentum space. This directly addresses the challenge of measuring and controlling coherent light–matter–electron interactions at the nanoscale. The delay- and momentum-dependent interference fringes validate phase locking and provide a pathway to quantify decoherence in practical geometries (loss of visibility for L > 40 µm). The agreement between experiment, full-wave simulations, and the analytical multi-path model underlines the physical picture of how EDPHS and electron-induced pathways combine in polaritonic samples. The approach is compact, compatible with continuous electron beams, and extends interferometric capabilities to non-paraxial, angle-resolved detection, which is crucial for polaritonics and nano-optics. These advances open opportunities for coherent control and correlation spectroscopy in quantum materials, including exciton–polaritons, and potentially for manipulating single quantum systems with nanoscale spatial resolution.

The work introduces and demonstrates a laser-free, internal-reference scheme for phase-locked photon–electron interaction in an electron microscope using an electron-driven photon source (EDPHS). The method achieves a degree of mutual coherence of ~27%, enabling spectral interferometry and retrieval of relative amplitude and phase maps in momentum–energy space. Experimental results, corroborated by FDTD simulations and an analytical four-path model, show controllable interference fringes versus delay and momentum, with coherent behavior up to L ≈ 40 µm and a temporal broadening of ~5.2 fs. This compact approach operates with continuous electron beams and paves the way for local photon–electron correlation spectroscopy of quantum materials and coherent exciton–polaritonic systems. Future directions include enhancing coherence by: (1) using aloof electron trajectories for EDPHS excitation to suppress incoherent CL; (2) cryogenic cooling to reduce phonon-related decoherence; (3) employing collimated, low-divergence electron beams. The technique could be extended to probe and coherently control quantum emitters, single-photon sources, and strongly coupled light–matter systems with nanometre spatial resolution.

• Decoherence reduces fringe visibility for L > 40 µm due to environmental interactions and incoherent relaxation channels.
• The current interferometry retrieves only the differential phase between sample and EDPHS radiation; absolute EDPHS phase is not measured.
• Incoherent CL contributions (random electron–hole pair generation, phonon relaxation) in both EDPHS and sample limit the degree of mutual coherence (~27%).
• The analytical model includes a limited set of scattering edges, leading to minor discrepancies with experiments that involve multiple edges.
• Reliable phase/amplitude retrieval depends on sufficient fringe visibility (most accurate for specific momentum ranges, e.g., 0.5k∥ ≤ k⊥ ≤ 0.8k∥) and clear separation of a.c./d.c. components.
• Geometry-specific requirements (e.g., edge scattering) facilitate coupling to EPs; generalization to other samples may require tailored structures.