Electrons herald non-classical light

Abstract

Free electrons are a widespread and universal source of electromagnetic fields. The past decades witnessed ever-growing control over many aspects of electron-generated radiation, from the incoherent emission produced by X-ray tubes to the exceptional brilliance of free-electron lasers. Reduced to the elementary process of quantized energy exchange between individual electrons and the electromagnetic field, electron beams may facilitate future sources of tunable quantum light. However, the quantum features of such radiation are tied to the correlation of the particles, calling for the joint electronic and photonic state to be explored for further applications. Here, we demonstrate the coherent parametric generation of non-classical states of light by free electrons. We show that the quantized electron energy loss heralds the number of photons generated in a dielectric waveguide. In Hanbury-Brown-Twiss measurements, an electron-heralded single-photon state is revealed via antibunching intensity correlations, while two-quantum energy losses of individual electrons yield pronounced two-photon coincidences. The approach facilitates the tailored preparation of higher-number Fock and other optical quantum states based on controlled interactions with free-electron beams.

Figures (4)

• Figure 1: Correlation measurement of waveguide-coupled photons and free electrons.a A beam of electrons passes a dielectric waveguide, generating photons that are guided and detected in a fiber-based HBT setup. The electron and photon arrival times are temporally correlated. b Enlarged sketch of the interaction region: The electron passes the waveguide surface at an impact parameter of around 250 nm to interact with the evanescent vacuum field of the waveguide modes. c Simulation of the photon spectral distribution generated in a $40\,\mu$m straight waveguide by 100-keV electrons (impact parameter 250 nm). Gray vertical lines: waveguide boundaries. d False-color image of an example photonic chip (scanning electron micrograph). The chip surface is covered with ITO (brighter surface: ITO on metal, darker surface: ITO on Si3N4 or on SiO2, side walls: SiO2) e Schematic of the correlated quantized electron energy loss and photon number. The electron (green) scatters at the optical mode, generating a random number of photons (red). After detection, the signal correlation links the photon number $k$ (vertical, blue) to the electron scattering order $m$ (horizontal, green). The generation process is expected to follow a Poissonian distribution.
• Figure 2: Three-particle correlation for one electron and two photons.a Schematic of the detection setup with the particle arrival times $t_\textrm{el}, t_\textrm{A}, t_\textrm{B}$ on the fiber-coupled photon detectors DA, DB and the electron detector Del and electron energy $E_\textrm{el}$ as measured parameters. The arrival times are correlated with each other. b Parameter space for threefold events. The data is analyzed through lineouts and integrals along different axes. c Bottom: Histogram of electron-photon-photon coincidence events $N_\textrm{e,A,B}$ as a function of $\tau_\textrm{A}$ and $E_\textrm{el}$, summed over $\tau_\textrm{B}$. Electron-photon scattering causes a coincidence peak at an electron energy shifted downward by around 0.9 eV. Top: The temporal coincidence uncertainty of around 2.9 ns FWHM represents the timing precision of electron detection. d Bottom: Histogram of particle triples as a function of time delay $t_\textrm{A}-t_\textrm{B}$ and electron energy $E_\textrm{el}$ filtered to true coincidences between a photon A and an electron. The coincidences are dominated by electrons that generated 2 photons. Top: The reduced timing uncertainty of 0.4 ns FWHM follows from the better time resolution in photon detection.
• Figure 3: Multiple scattering and heralded electron spectra.a Time-averaged (not photon-correlated) electron spectrum (blue), modeled (red) by cascaded $m$-photon multiple-loss peaks (yellow) and an exponentially decaying continuum. b Sketch of the electron-beam caustic traversing the waveguide with a convergence half-angle of $\alpha=1.1$ mrad, causing some spatial averaging of the coupling constant. c Experimentally observed decay of the mean coupling strength towards larger impact parameters (distance to the waveguide). The standard deviation is given as a gray background. The peak height distributions at different $g^\textrm{EELS}_0$ are included as insets. d Energy distributions of uncorrelated (blue) and correlated electrons (red, yellow) for $k$ detected photons (normalized to the area under the curves). The correlated spectra are obtained by summing over the background-subtracted coincidence peaks shown in Figures \ref{['fig:figure2_correlation']}c,d. e Measured optical spectrum with a central peak width of about 80 nm, or 65 meV, normalized to the maximum value.
• Figure 4: Statistical analysis of generated photons. a,b Electron-photon-photon correlation events $N_\textrm{e,A,B}$ as a function of photon-electron time delays, selected by electron energy: a scattering order $m=1$, and b scattering order $m=2$. c Violation of the Cauchy-Schwartz Inequality ($\gamma > 1$) for the electron-photon interaction at different time delays $\tau$ (points connected for visibility). d Unheralded photon-photon intensity correlation for varying electron current. e Electron-heralded photon-photon intensity correlation filtered to the energy region $m=1$ as a function of both time delays. Inset: Time-averaged $g^{(2)}$ for $m=1$. f Photon-photon intensity correlation as a function of the number of photon-heralding electrons $q$ between the two heralded photons without energy selection (top) and for $m=1$ (bottom).