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Free electron beams and their quantum coupling with photons is attracting a rising interest due to the basic questions it addresses and the cutting-edge technology these particles are involved in, such as microscopy, spectroscopy, and quantum computation. This work investigates theoretically the concept of electron-photon coupling in the spatial domain. Their interaction is discussed as a thought experiment of spontaneous photon emission from a dual-path free-electron (free-e) beam. We discuss a retro-causal paradox that may emerge from naively extending perceptions of single-path e-photon coupling to transversely separated paths, and its resolution through the physics of two-particle interference. The precise spatial control of electrons and photons within e-microscopes enables manipulation of their respective states, thus, such instruments can harness position-encoded free-e qubits for novel quantum sensing and the transfer of quantum information., Comment: 10 pages, 2 figures

The advent of ultrafast science with pulsed electron beams raised the need in controlling the temporal features of the electron pulses. One promising suggestion is the nano-selective quantum optics with multi-electrons, which scales quadratically with the number of electrons within the coherence time of the quantum system. Terahertz (THz) radiation from optical nonlinear crystals is an attractive methodology to generate the rapidly varying electric fields necessary for electron compression, with an advantage of an inherent temporal locking to laser-triggered electrons, such as in untrafast electron microscopes. Longer (picosecond-) pulses require sub-THz field for their compression, however, the generation of such low frequencies require pumping with energetic optical pulses and their focusability is fundamentally limited by their mm-wavelength. This work proposes electron-pulse compression with sub-THz fields directly in the vicinity of their dipolar origin, thereby avoiding mediation through radiation. We analyze the merits of nearfields for compression of slow electrons particularly in challenging regimes for THz radiation, such as small numerical apertures, micro-joule-level optical pump pulses, and low frequencies. This sheme can be implemented within the tight constraints of electron microscopes and reach fiels of a few kV/cm below 0.1 THz at high repetition rates. Our paradigm offers a realistic approach for controlling electron pulses spatially and temporally in many experiments, opening the path of flexible multi-electron manipulation for analytic and quantum sciences., Comment: 22 pages, 3 figures

Recently, integrated photonic circuits have brought new capabilities to electron microscopy and been used to demonstrate efficient electron phase modulation and electron-photon correlations. Here, we quantitatively analyze the feasibility of high fidelity and high purity quantum state heralding using a free electron and a photonic integrated circuit with parametric coupling, and propose schemes to shape useful electron and photonic states in different application scenarios. Adopting a dissipative quantum electrodynamics treatment, we formulate a framework for the coupling of free electrons to waveguide spatial-temporal modes. To avoid multimode-coupling induced state decoherence, we show that with proper waveguide design, the interaction can be reduced to a single-mode coupling to a quasi-TM00 mode. In the single-mode coupling limit, we go beyond the conventional state ladder treatment, and show that the electron-photon energy correlations within the ladder subspace can still lead to a fundamental purity and fidelity limit on complex optical and electron state preparations through heralding schemes. We propose applications that use this underlying correlation to their advantage, but also show that the imposed limitations for general applications can be overcome by using photonic integrated circuits with an experimentally feasible interaction length, showing its promise as a platform for free-electron quantum optics.

Spontaneous processes triggered in a sample by free electrons are commonly regarded as incoherent, and therefore unable to interfere with external light sources. Here, we challenge this concept by showing through first-principles theory that light and free-electron pulses can interfere when interacting with a nanostructure, giving rise to a modulation in the spectral distribution of the cathodoluminescence light emission that is strongly dependent on the electron wave function. Specifically, for a temporally focused electron, cathodoluminescence can be cancelled upon illumination with a spectrally modulated dimmed laser that is phase-locked relative to the electron density profile. We illustrate this idea with realistic simulations under attainable conditions in currently available ultrafast electron microscopes. We further argue that the interference between excitations produced by light and free electrons opens a new window to manipulate the ultrafast materials response by combining the spectral and temporal selectivity of the light with the atomic resolution of electron beams., Comment: 26 pages, 7 figures, 87 references

Strong interference in ultrathin film semiconductor absorbers on metallic back reflectors has been shown to enhance the light harvesting efficiency of solar cell materials. However, metallic back reflectors are not suitable for tandem cell configurations because photons cannot be transmitted through the device. Here, we introduce a method to implement strong interference in ultrathin film top absorbers in a tandem cell configuration through use of distributed Bragg reflectors (DBRs). We showcase this by designing and fabricating a photoelectrochemical-photovoltaic (PEC-PV) stacked tandem cell in a V-shaped configuration where short wavelength photons are reflected back to the photoanode material (hematite, Fe2O3), whereas long wavelength photons are transmitted to the bottom silicon PV cell. We employ optical simulations to determine the optimal thicknesses of the DBR layers and the V-shape angle to maximize light absorption in the ultrathin (10 nm thick) hematite film. The DBR spectral response can be tailored to allow for a more than threefold enhancement in absorbed photons compared to a layer of the same thickness on transparent current collectors. Using a DBR to couple a bottom silicon PV cell with an ultrathin hematite top PEC cell, we demonstrate unassisted solar water splitting and show that DBRs can be designed to enhance strong interference in ultrathin films while enabling stacked tandem cell configuration.

Light-induced magnetization changes, such as all-optical switching, skyrmion nucleation, and intersite spin transfer, unfold on temporal and spatial scales down to femtoseconds and nanometers, respectively. Pump-probe spectroscopy and diffraction studies indicate that spatio-temporal dynamics may drastically affect the non-equilibrium magnetic evolution. Yet, direct real-space magnetic imaging on the relevant timescale has remained challenging. Here, we demonstrate ultrafast high-harmonic nanoscopy employing circularly polarized high-harmonic radiation for real-space imaging of femtosecond magnetization dynamics. We observe the reversible and irreversible evolution of nanoscale spin textures following femtosecond laser excitation. Specifically, we map quenched magnetic domains and localized spin structures in Co/Pd multilayers with a sub-wavelength spatial resolution down to 16 nm, and strobosocopically trace the local magnetization dynamics with 40 fs temporal resolution. Our approach enables the highest spatio-temporal resolution of magneto-optical imaging to date. Facilitating ultrafast imaging with an extreme sensitivity to various microscopic degrees of freedom expressed in chiral and linear dichroism, we envisage a wide range of applications spanning magnetism, phase transitions, and carrier dynamics., Comment: 14 pages, 4 figures

We investigate theoretically the quantum-coherence properties of the cathodoluminescence (CL) emission produced by a temporally modulated electron beam. Specifically, we consider the quantum-optical correlations of CL from electrons that are previously shaped by a laser field. The main prediction here is the presence of phase correlations between the emitted CL field and the electron-modulating laser, even though the emission intensity and spectral profile are independent of the electron state. In addition, the coherence of the CL field extends to harmonics of the laser frequency. Since electron beams can be focused to below one Angstrom, their ability to transfer optical coherence could enable ultra precise excitation, manipulation, and spectroscopy of nanoscale quantum systems., Comment: 8 pages (16 pages including appendices), 3 figures

Strong-field methods in solids enable new strategies for ultrafast nonlinear spectroscopy and provide all-optical insights into the electronic properties of condensed matter in reciprocal and real space. Additionally, solid-state media offers unprecedented possibilities to control high-harmonic generation using modified targets or tailored excitation fields. Here we merge these important points and demonstrate circularly-polarized high-harmonic generation with polarization-matched excitation fields for spectroscopy of chiral electronic properties at surfaces. The sensitivity of our approach is demonstrated for structural helicity and termination-mediated ferromagnetic order at the surface of silicon-dioxide and magnesium oxide, respectively. Circularly polarized radiation emanating from a solid sample now allows to add basic symmetry properties as chirality to the arsenal of strong-field spectroscopy in solids. Together with its inherent temporal (femtosecond) resolution and non-resonant broadband spectrum, the polarization control of high harmonics from condensed matter can illuminate ultrafast and strong field dynamics of surfaces, buried layers or thin films., Comment: 24 pages, 5 figures

Circular dichroism spectroscopy is an essential technique for understanding molecular structure and magnetic materials, but spatial resolution is limited by the wavelength of light, and sensitivity sufficient for single-molecule spectroscopy is challenging. We demonstrate that electrons can efficiently measure the interaction between circularly polarized light and chiral materials with deeply sub-wavelength resolution. By scanning a nanometer-sized focused electron beam across an optically-excited chiral nanostructure and measuring the electron energy spectrum at each probe position, we produce a high-spatial-resolution map of near-field dichroism. This technique offers a nanoscale view of a fundamental symmetry and could be employed as "photon staining" to increase biomolecular material contrast in electron microscopy.

Free-electron beams serve as uniquely versatile probes of microscopic structure and composition, and have repeatedly revolutionized atomic-scale imaging, from solid-state physics to structural biology. Over the past decade, the manipulation and interaction of electrons with optical fields has seen significant progress, enabling novel imaging methods, schemes of near-field electron acceleration, and culminating in 4D microscopy techniques with both high temporal and spatial resolution. However, weak coupling strengths of electron beams to optical excitations are a standing issue for existing and emerging applications of optical free-electron control. Here, we demonstrate phase matched near-field coupling of a free-electron beam to optical whispering gallery modes of dielectric microresonators. The cavity-enhanced interaction with these optically excited modes imprints a strong phase modulation on co-propagating electrons, which leads to electron-energy sidebands up to hundreds of photon orders and a spectral broadening of 700 eV. Mapping the near-field interaction with ultrashort electron pulses in space and time, we trace the temporal ring-down of the microresonator following a femtosecond excitation and observe the cavity's resonant spectral response. Resonantly enhancing the coupling of electrons and light via optical cavities, with efficient injection and extraction, can open up novel applications such as continuous-wave acceleration, attosecond structuring, and real-time all-optical electron detection., Comment: 11 pages, 3 figures

This work sets a road-map towards an experimental realization of strong coupling between free-electrons and photons, and analytically explores entanglement phenomena that emerge in this regime. The proposed model unifies the strong-coupling predictions with known electron-photon interactions. Additionally, this work predicts a non-Columbic entanglement between freely propagating electrons. Since strong-coupling can map entanglements between photon pairs onto photon-electron pairs, it may harness electron beams for quantum communication, thus far exclusive to photons., Comment: 12 pages, 4 figures. Supplementary 21 pages. This version is shortened substantially, and more stress is placed on the properties of the electron-photon entanglement, with electron-electron entanglement as an example. Typos corrected

This work demonstrates nanoscale magnetic imaging using bright circularly polarized high-harmonic radiation. We utilize the magneto-optical contrast of worm-like magnetic domains in a Co/Pd multilayer structure, obtaining quantitative amplitude and phase maps by lensless imaging. A diffraction-limited spatial resolution of 49 nm is achieved with iterative phase reconstruction enhanced by a holographic mask. Harnessing the unique coherence of high harmonics, this approach will facilitate quantitative, element-specific and spatially-resolved studies of ultrafast magnetization dynamics, advancing both fundamental and applied aspects of nanoscale magnetism., Comment: Ofer Kfir and Sergey Zayko contributed equally to this work. Presented in CLEO 2017 (Oral) doi.org/10.1364/CLEO_QELS.2017.FW1H.8

We predict high-order harmonics in which the polarization within the spectral bandwidth of each harmonic varies continuously and significantly. For example, the interaction of counter-rotating circularly-polarized bichromatic drivers having close central frequencies with isotropic gas leads to the emission of polarization-fan harmonics which are nearly circularly-polarized in one tail of the harmonic peak, linear in the center of the peak and nearly circular with the opposite helicity in the opposite tail. Polarization fan harmonics are obtained as a result of multiple (at least two) head-on recollisions of electrons with their parent ions occurring from different angles. The process can be phase-matched using standard methods (e.g. pressure tuning phase matching) and maintains the single-atom polarization property through propagation. These polarization-fan harmonics may be used for exploring non-repetitive ultrafast chiral phenomena, e.g. dynamics of magnetic domains, in a single shot, Comment: 10 pages, 5 figures

Circularly-polarized extreme UV and X-ray radiation provides valuable access to the structural, electronic and magnetic properties of materials. To date, this capability was available only at large-scale X-ray facilities such as synchrotrons. Here we demonstrate the first bright, phase-matched, extreme UV circularly-polarized high harmonics and use this new light source for magnetic circular dichroism measurements at the M-shell absorption edges of Co. We show that phase matching of circularly-polarized harmonics is unique and robust, producing a photon flux comparable to the linearly polarized high harmonic sources that have been used very successfully for ultrafast element-selective magneto-optic experiments. This work thus represents a critical advance that makes possible element-specific imaging and spectroscopy of multiple elements simultaneously in magnetic and other chiral media with very high spatial and temporal resolution, using tabletop-scale setups., Comment: 12 text pages, 4 figures, supplamentary information 6 pages

High harmonic generation (HHG) is a unique and useful process in which infrared or visible radiation is frequency up converted into the extreme ultraviolet and x ray spectral regions. As a parametric process, high harmonic generation should conserve the radiation energy, momentum and angular momentum. Indeed, conservation of energy and momentum have been demonstrated. Angular momentum of optical beams can be divided into two components: orbital and spin (polarization). Orbital angular momentum is assumed to be conserved and recently observed deviations were attributed to propagation effects. On the other hand, conservation of spin angular momentum has thus far never been studied, neither experimentally nor theoretically. Here, we present the first study on the role of spin angular momentum in extreme nonlinear optics by experimentally generating high harmonics of bi chromatic elliptically polarized pump beams that interact with isotropic media. While observing that the selection rules qualitatively correspond to spin conservation, we unequivocally find that the process of converting pump photons into a single high-energy photon does not conserve angular momentum, i.e. this process is not self contained. In one regime, we numerically find that this major fundamental discrepancy can be explained if the harmonic photons are emitted in pairs. Yet in another regime, the ionizing electron carries the missing angular momentum. The results presented here, apart from exploring the very foundations of HHG, are also important for a variety of applications, as our system exhibits full control over the harmonics polarization, from circular through elliptical to linear polarization, without comprising the efficiency of the process. This work paves the way for a broad range of applications with HHG, from ultrafast circular dichroism to zepto-clocks and to attosecond quantum optics.

We propose lattice soleakons: self-trapped waves that self-consistently populate leaky modes of their self-induced defects in periodic potentials. Two types, discrete and Bragg, lattice soleakons are predicted. Discrete soleakons that are supported by combination of self-focusing and self-defocusing nonlinearities propagate robustly for long propagation distances. They eventually abruptly disintegrate because they emit power to infinity at an increasing pace. In contrast, Bragg soleakons self-trap by only self-focusing, and they do not disintegrate because they emit power at a decreasing rate.