Nonclassical states of light, such as photon number states, are crucial in multiple regions of quantum technology. However, many states are still difficult to achieve. A potential new source of quantum states is free electron scattering. Especially coherent, parametric cathodoluminescence preserves the quantum phase between free electrons and light and enables wavelength tuning. Here, we demonstrate the generation of nonclassical multiphoton states via coherent cathodoluminescence, correlating electrons and photons in time and energy. We characterize the electron-heralded photons, observing the correlation between the electron energy loss and generated photon number and measuring an antibunching behavior in the electron-heralded optical intensity correlation. In the future, this combination of cathodoluminescence and correlation detection may form a versatile source of complex quantum photon states.
Nonclassical states of light, such as photon number states, are crucial in multiple regions of quantum technology. However, many states are still difficult to achieve. A potential new source of quantum states is free electron scattering. Especially coherent, parametric cathodoluminescence preserves the quantum phase between free electrons and light and enables wavelength tuning. Here, we demonstrate the generation of nonclassical multiphoton states via coherent cathodoluminescence, correlating electrons and photons in time and energy. We characterize the electron-heralded photons, observing the correlation between the electron energy loss and generated photon number and measuring an antibunching behavior in the electron-heralded optical intensity correlation. In the future, this combination of cathodoluminescence and correlation detection may form a versatile source of complex quantum photon states.
Abstract Free electrons are a universal source of electromagnetic fields, and fundamentally their quantized energy exchange may facilitate generating tunable quantum light. Because the quantum features of the emitted radiation are encoded in the joint electronic and photonic state, they can only be revealed by a measurement accessing both subsystems. Here we demonstrate the coherent parametric generation of such non-classical states of light by free electrons. Investigating electron–photon correlations, we show that the quantized electron energy loss heralds the number of photons generated in a dielectric waveguide. In Hanbury Brown–Twiss measurements, we observe an electron-heralded single-photon state using antibunching intensity correlation, whereas two-quantum energy losses of individual electrons yield pronounced two-photon coincidences. Our results will enable the tailored preparation of higher-number Fock and other optical quantum states on the basis of controlled interactions with free-electron beams.
Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (λ/2), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).
Electron beams are an exceptional tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled nanoscale [2,3] and attosecond phase-resolved mapping of optical near-fields [4] by stimulated inelastic scattering between electrons and light. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [5]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promoting single-particle-based scattering experiments [6]. Here, we demonstrate the generation of nonclassical multiphoton states via coherent cathodoluminescence (CL) from an optical waveguide, approaching near-unity coupling in electron spectroscopy of nanophotonic systems [7]. To this end, we scatter swift electrons at the optical mode of a custom silicon nitride photonic chip. Specifically, inside of a transmission electron microscope, a beam of free electrons (100-keV kinetic energy) passes parallel to the waveguide surface in an aloof geometry (cf. Fig. 1a). The electrons can inelastically scatter with the evanescent tail of the guided optical mode, generating photons at a wavelength around 1400 nm in the fundamental quasi-TM mode, while the electrons lose multiples N of the corresponding photon energy of 0.88 eV (cf. Fig. 1b). The photons are then coupled via optical fibers to a balanced beam splitter and two single-photon avalanche diodes (SPADs), implementing a Hanbury Brown and Twiss (HBT) setup (cf. Fig. 1c). Probing the ensemble average using the 2nd-order correlation function g(2), we observe Poissonian photon statistics in accordance with the underlying coherent scattering mechanism (Fig. 1d, top). A parallel single-particle-resolved measurement using an event-based electron camera (Timepix3 ASIC) coupled to an EEL spectrometer provides information on both electron energy and arrival time. This allows us to further investigate the photon statistics of the generated light as a function of the electron energy. Using this electron-heralded HBT setup, we verify the generation of single photons following an energy loss of E = ℏω (Fig. 1d, bot), and photon pairs for double scattering events. Characterizing the electron-driven photon generation using established metrics for heralded single-photon sources, such as spontaneous parametric down-conversion (SPDC), we find an intrinsic single-photon heralding efficiency of 10% and a coincidence-to-accidental ratio > 30. This establishes a new source for electron-heralded quantum light, which may find its applications in quantum photonics. Practically, efficient electron-photon coupling and event-based detention, offers a new pathway for coincidence-enhanced electron spectroscopy of photonic materials [8]. Besides eliminating undesired and formerly unrecoverable averaging, access to the full scattering distribution of the involved particles can strongly suppress noise in ultrafast electron experiments [6]. Furthermore, for systems that can be directly pumped by single electrons, ultrafast dynamics can be studied using continuous electron beams, achieving sub-nanosecond resolution, only limited by the employed detector technology. Finally, this work represent an essential step toward quantum-enhanced electron imaging and enables the heralding of individual electrons for dose-sensitive applications. a) Electrons are scattered at an extended waveguide, generating light by coherent cathodoluminescence. b) Electron energy loss into discrete sidebands is observed, spaced by the photon energy ℏω. c) Event-based coincidence spectroscopy enables electron-heralded detection of photon number states. d) The discrete 2nd-order correlation function g(2)[q] shows Poissonian statistics for unheralded photon detection, while conditioning on an ℏω energy loss produces high-contrast single-photon states.
The quantum properties of matter and radiation can be leveraged to surpass classical limits of sensing and detection. Quantum optics does so by creating and measuring nonclassical light. However, better performance requires higher photon-number states, which are challenging to generate and detect. Here, we combine photons and free electrons to solve the problem of generating and detecting high-number states well beyond those reachable with light alone and further show that an unprecedented level of sensitivity and resolution is gained based on the measurement of free-electron currents after suitably designed electron-light interactions. Our enabling ingredient is the strong electron-light coupling produced by aloof electron reflection on an optical waveguide, leading to the emission or absorption of a high number of guided photons by every single electron. We establish through rigorous theory that, by combining electron-beam splitters with two electron-waveguide interactions, the sensitivity to detect optical-phase changes can be enhanced dramatically using currently attainable technology. These results inaugurate a disruptive quantum technology relying on free electrons and their strong interaction with waveguided light.
Advancing quantum information and communication requires the control of quantum correlations in complementary degrees of freedom. In this work, we generate electron-photon pair states via inelastic scattering of free electrons at a high-Q photonic-chip-based microresonator. In analogy to spontaneous parametric down-conversion, time- and energy-resolved detection of both particles enables various heralding schemes. We experimentally characterize this new heralded source of single photons and free electrons. Ultimately, these results underpin the recent progress in free-electron quantum optics, promising electron-photon entanglement, tailored photon Fock states, and quantum-enhanced electron imaging.
Harnessing a beam of slow free electrons in artificial photonic structures offers a powerful, tunable platform for generating nonclassical light without the need for heavy physical equipment. Here we present a theory of nonclassical lasing, demonstrating how incoherent electrons in photonic crystal cavities can coherently emit photons through collective dynamics. When photon emission rate exceeds cavity losses, nonclassical lasing with sub-Poissonian photon statistics emerges, driven by multi-photon Rabi oscillations. At specific coupling strengths, quantum state trapping effect emerges, producing high-fidelity Fock states at room temperature (e.g. nearly 90%-fidelity of four photon Fock state). Notably, the frequency of the emitted photons can be readily tuned via the velocity of the injected electrons to match cavity modes. This approach supports photonic integration and offers a scalable, energy-efficient platform for room-temperature quantum light sources and advanced studies in quantum electrodynamics.