Shaping quantum photonic states using free electrons

Strongly correlated multielectron bunches from interaction with quantum light

Strongly correlated electron systems are a cornerstone of modern physics, being responsible for groundbreaking phenomena from superconducting magnets to quantum computing. In most cases, correlations in electrons arise exclusively because of Coulomb interactions. In this work, we reveal that free electrons interacting simultaneously with a light field can become highly correlated via mechanisms beyond Coulomb interactions. In the case of two electrons, the resulting Pearson correlation coefficient for the joint probability distribution of the output electron energies is enhanced by more than 13 orders of magnitude compared to that of electrons interacting with the light field in succession (one after another). These highly correlated electrons are the result of momentum and energy exchange between the participating electrons via the external quantum light field. Our findings pave the way to the creation and control of highly correlated free electrons for applications including quantum information and ultrafast imaging.

Topologically Protected Strong-Interaction of Photonics with Free Electrons

We propose a robust scheme of studying the strong interactions between free electrons and photons using topological photonics. Our study reveals that the topological corner state can be used to enhance the interaction between light and a free electron significantly. The quality factor of the topological cavity can exceed 20 000 and the corner state has a very long lifetime even after the pump pulse is off. And thus, the platform enables us to achieve a strong interaction without the need for zero delay and phase matching as in traditional photon-induced near-field electron microscopy (PINEM). This work provides the new perspective that the topological photonic structures can be utilized as a platform to shape free electron wave packets, which facilitates the control of quantum electrodynamical (QED) processes and quantum optics with free electrons in the future.

Space-qualifying silicon photonic modulators and circuits

Reducing the form factor while retaining the radiation hardness and performance matrix is the goal of avionics. While a compromise between a transistor's size and its radiation hardness has reached consensus in microelectronics, the size-performance balance for their optical counterparts has not been quested but eventually will limit the spaceborne photonic instruments' capacity to weight ratio. Here, we performed space experiments of photonic integrated circuits (PICs), revealing the critical roles of energetic charged particles. The year-long cosmic radiation exposure does not change carrier mobility but reduces free carrier lifetime, resulting in unchanged electro-optic modulation efficiency and well-expanded optoelectronic bandwidth. The diversity and statistics of the tested PIC modulator indicate the minimal requirement of shielding for PIC transmitters with small footprint modulators and complexed routing waveguides toward lightweight space terminals for terabits communications and intersatellite ranging.

Intense Squeezed Light from Lasers with Sharply Nonlinear Gain at Optical Frequencies

Nonclassical states of light, such as number-squeezed light, with fluctuations below the classical shot noise level, have important uses in metrology, communication, quantum information processing, and quantum simulation. However, generating these nonclassical states of light, especially with high intensity and a high degree of squeezing, is challenging. To address this problem, we introduce a new concept which uses gain to generate intense sub-Poissonian light at optical frequencies. It exploits a strongly nonlinear gain for photons which arises from a combination of frequency-dependent gain and Kerr nonlinearity. In this laser architecture, the interaction between the gain medium and Kerr nonlinearity suppresses the spontaneous emission at high photon number states, leading to a strong "negative feedback" that suppresses photon-number fluctuations. We discuss realistic implementations of this concept based on the use of solid-state gain media in laser cavities with Kerr nonlinear materials, showing how 90% squeezing of photon number fluctuations below the shot noise level can be realized.

Generating optical cat states via quantum interference of multi-path free-electron-photons interactions

The novel quantum effects induced by the free-electron-photons interaction have attracted increasing interest due to their potential applications in ultrafast quantum information processing. Here, we propose a scheme to generate optical cat states based on the quantum interference of multi-path free-electron-photons interactions that take place simultaneously with strong coupling strength. By performing a projection measurement on the electron, the state of light changes significantly from a coherent state into a non-Gaussian state with either Wigner negativity or squeezing property, both possess metrological power to achieve quantum advantage. More importantly, we show that the Wigner negativity oscillates with the coupling strength, and the optical cat states are successfully generated with high fidelity at all the oscillation peaks. This oscillation reveals the quantum interference effect of the multiple quantum pathways in the interaction of the electron with photons, by that various nonclassical states of light are promising to be fast prepared and manipulated. These findings inspire further exploration of emergent quantum phenomena and advanced quantum technologies with free electrons.

Efficient coupling between free electrons and the supermode of a silicon slot waveguide

Laser light can modulate the kinetic energy spectrum of free electrons and induce extremely high acceleration gradients, which are instrumental to electron microscopy and electron acceleration, respectively. We present a design scheme for a silicon photonic slot waveguide which hosts a supermode to interact with free electrons. The efficiency of this interaction relies on the coupling strength per photon along the interaction length. We predict an optimum value of 0.4266, resulting in the maximum energy gain of 28.27 keV for an optical pulse energy of only 0.22 nJ and duration 1 ps. The acceleration gradient is 1.05 GeV/m, which is lower than the maximum imposed by the damage threshold of Si waveguides. Our scheme shows how the coupling efficiency and energy gain can be maximized without maximizing the acceleration gradient. It highlights the potential of silicon photonics technology in hosting electron-photon interactions with direct applications in free-electron acceleration, radiation sources, and quantum information science.

Jaynes-Cummings interaction between low-energy free electrons and cavity photons

The Jaynes-Cummings Hamiltonian is at the core of cavity quantum electrodynamics; however, it relies on bound-electron emitters fundamentally limited by the binding Coulomb potential. In this work, we propose theoretically a new approach to realizing the Jaynes-Cummings model using low-energy free electrons coupled to dielectric microcavities and exemplify several quantum technologies made possible by this approach. Using quantum recoil, a large detuning inhibits the emission of multiple consecutive photons, effectively transforming the free electron into a few-level system coupled to the cavity mode. We show that this approach can be used for generation of single photons, photon pairs, and even a quantum SWAP gate between a photon and a free electron, with unity efficiency and high fidelity. Tunable by their kinetic energy, quantum free electrons are inherently versatile emitters with an engineerable emission wavelength. Hence, they pave the way toward new possibilities for quantum interconnects between photonic platforms at disparate spectral regimes.

Creating large Fock states and massively squeezed states in optics using systems with nonlinear bound states in the continuum

The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n-photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n (n >  10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.

Quantum sensing of strongly coupled light-matter systems using free electrons

Strong coupling in light-matter systems is a central concept in cavity quantum electrodynamics and is essential for many quantum technologies. Especially in the optical range, full control of highly connected multi-qubit systems necessitates quantum coherent probes with nanometric spatial resolution, which are currently inaccessible. Here, we propose the use of free electrons as high-resolution quantum sensors for strongly coupled light-matter systems. Shaping the free-electron wave packet enables the measurement of the quantum state of the entire hybrid systems. We specifically show how quantum interference of the free-electron wave packet gives rise to a quantum-enhanced sensing protocol for the position and dipole orientation of a subnanometer emitter inside a cavity. Our results showcase the great versatility and applicability of quantum interactions between free electrons and strongly coupled cavities, relying on the unique properties of free electrons as strongly interacting flying qubits with miniscule dimensions.

Photonic flatband resonances for free-electron radiation

Flatbands have become a cornerstone of contemporary condensed-matter physics and photonics. In electronics, flatbands entail comparable energy bandwidth and Coulomb interaction, leading to correlated phenomena such as the fractional quantum Hall effect and recently those in magic-angle systems. In photonics, they enable properties including slow light1 and lasing2. Notably, flatbands support supercollimation-diffractionless wavepacket propagation-in both systems3,4. Despite these intense parallel efforts, flatbands have never been shown to affect the core interaction between free electrons and photons. Their interaction, pivotal for free-electron lasers5, microscopy and spectroscopy6,7, and particle accelerators8,9, is, in fact, limited by a dimensionality mismatch between localized electrons and extended photons. Here we reveal theoretically that photonic flatbands can overcome this mismatch and thus remarkably boost their interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the associated free-electron radiation by tuning their trajectory and velocity. We observe signatures of flatband enhancement, recording a two-order increase from the conventional diffraction-enabled Smith-Purcell radiation. The enhancement enables polarization shaping of free-electron radiation and characterization of photonic bands through electron-beam measurements. Our results support the use of flatbands as test beds for strong light-electron interaction, particularly relevant for efficient and compact free-electron light sources and accelerators.

Optical-cavity mode squeezing by free electrons

The generation of nonclassical light states bears a paramount importance in quantum optics and is largely relying on the interaction between intense laser pulses and nonlinear media. Recently, electron beams, such as those used in ultrafast electron microscopy to retrieve information from a specimen, have been proposed as a tool to manipulate both bright and dark confined optical excitations, inducing semiclassical states of light that range from coherent to thermal mixtures. Here, we show that the ponderomotive contribution to the electron-cavity interaction, which we argue to be significant for low-energy electrons subject to strongly confined near-fields, can actually create a more general set of optical states, including coherent and squeezed states. The postinteraction electron spectrum further reveals signatures of the nontrivial role played by A ² terms in the light-matter coupling Hamiltonian, particularly when the cavity is previously excited by either chaotic or coherent illumination. Our work introduces a disruptive approach to the creation of nontrivial quantum cavity states for quantum information and optics applications, while it suggests unexplored possibilities for electron beam shaping.

Cavity-mediated electron-photon pairs

Quantum information, communication, and sensing rely on the generation and control of quantum correlations in complementary degrees of freedom. Free electrons coupled to photonics promise novel hybrid quantum technologies, although single-particle correlations and entanglement have yet to be shown. In this work, we demonstrate the preparation of electron-photon pair states using the phase-matched interaction of free electrons with the evanescent vacuum field of a photonic chip-based optical microresonator. Spontaneous inelastic scattering produces intracavity photons coincident with energy-shifted electrons, which we employ for noise-suppressed optical mode imaging. This parametric pair-state preparation will underpin the future development of free-electron quantum optics, providing a route to quantum-enhanced imaging, electron-photon entanglement, and heralded single-electron and Fock-state photon sources.

Quantum-Coherent Light-Electron Interaction in a Scanning Electron Microscope

The last two decades experimentally affirmed the quantum nature of free electron wave packets by the rapid development of transmission electron microscopes into ultrafast, quantum-coherent systems. So far, all experiments were restricted to the bounds of transmission electron microscopes enabling one or two photon-electron interaction sites. We show the quantum coherent coupling between electrons and light in a scanning electron microscope, at unprecedentedly low, subrelativistic energies down to 10.4 keV. These microscopes not only afford the yet-unexplored energies from ∼0.5 to 30 keV providing the optimum electron-light coupling efficiency, but also offer spacious and easily configurable experimental chambers for extended, cascaded optical set ups, potentially boasting thousands of photon-electron interaction sites. Our results make possible experiments in electron wave packet shaping, quantum computing, and spectral imaging with low-energy electrons.

Integrated photonics enables continuous-beam electron phase modulation

Integrated photonics facilitates extensive control over fundamental light-matter interactions in manifold quantum systems including atoms1, trapped ions2,3, quantum dots4 and defect centres5. Ultrafast electron microscopy has recently made free-electron beams the subject of laser-based quantum manipulation and characterization6-11, enabling the observation of free-electron quantum walks12-14, attosecond electron pulses10,15-17 and holographic electromagnetic imaging18. Chip-based photonics19,20 promises unique applications in nanoscale quantum control and sensing but remains to be realized in electron microscopy. Here we merge integrated photonics with electron microscopy, demonstrating coherent phase modulation of a continuous electron beam using a silicon nitride microresonator. The high-finesse (Q0 ≈ 106) cavity enhancement and a waveguide designed for phase matching lead to efficient electron-light scattering at extremely low, continuous-wave optical powers. Specifically, we fully deplete the initial electron state at a cavity-coupled power of only 5.35 microwatts and generate >500 electron energy sidebands for several milliwatts. Moreover, we probe unidirectional intracavity fields with microelectronvolt resolution in electron-energy-gain spectroscopy21. The fibre-coupled photonic structures feature single-optical-mode electron-light interaction with full control over the input and output light. This approach establishes a versatile and highly efficient framework for enhanced electron beam control in the context of laser phase plates22, beam modulators and continuous-wave attosecond pulse trains23, resonantly enhanced spectroscopy24-26 and dielectric laser acceleration19,20,27. Our work introduces a universal platform for exploring free-electron quantum optics28-31, with potential future developments in strong coupling, local quantum probing and electron-photon entanglement.

Measurement of Temporal Coherence of Free Electrons by Time-Domain Electron Interferometry

The temporal properties of an electron beam are decisive for modern ultrafast electron microscopy and for the quantum optics of the free electron in laser fields. Here, we report a time-domain interferometer that measures and distinguishes the pure and ensemble coherences of a free-electron beam in a transmission electron microscope via symmetry-breaking shifts of photon-order sideband peaks. This result is a free-electron analog to the reconstruction of attosecond busts and photoemission delays in optical attosecond spectroscopy. We find a substantial pure electron coherence that is connected to the thermodynamics of the emitter material and a lower ensemble coherence that is governed by space-charge effects. Pure temporal coherences above 5 fs are measured at >10^{9} electrons per second in a high-brightness beam.

Imprinting the quantum statistics of photons on free electrons

[Figure: see text].

Superradiance and Subradiance due to Quantum Interference of Entangled Free Electrons

When multiple quantum emitters radiate, their emission rate may be enhanced or suppressed due to collective interference in a process known as super- or subradiance. Such processes are well known to occur also in light emission from free electrons, known as coherent cathodoluminescence. Unlike atomic systems, free electrons have an unbounded energy spectrum, and, thus, all their emission mechanisms rely on electron recoil, in addition to the classical properties of the dielectric medium. To date, all experimental and theoretical studies of super- and subradiance from free electrons assumed only classical correlations between particles. However, dependence on quantum correlations, such as entanglement between free electrons, has not been studied. Recent advances in coherent shaping of free-electron wave functions motivate the investigation of such quantum regimes of super- and subradiance. In this Letter, we show how a pair of coincident path-entangled electrons can demonstrate either super- or subradiant light emission, depending on the two-particle wave function. By choosing different free-electron Bell states, the spectrum and emission pattern of the light can be reshaped, in a manner that cannot be accounted for by a classical mixed state. We show these results for light emission in any optical medium and discuss their generalization to many-body quantum states. Our findings suggest that light emission can be sensitive to the explicit quantum state of the emitting matter wave and possibly serve as a nondestructive measurement scheme for measuring the quantum state of many-body systems.

Modulation of Cathodoluminescence Emission by Interference with External Light

Spontaneous processes triggered in a sample by free electrons, such as cathodoluminescence, are commonly regarded and detected as stochastic events. Here, we supplement this picture 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 canceled 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 enables the manipulation of the ultrafast materials response by combining the spectral and temporal selectivity of the light with the atomic resolution of electron beams.

Optical Excitations with Electron Beams: Challenges and Opportunities

Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron energy losses and cathodoluminescence light emission. In combination with ultrafast optics, the emerging field of ultrafast electron microscopy utilizes synchronized femtosecond electron and light pulses that are aimed at the sampled structures, holding the promise to bring simultaneous sub-Å-sub-fs-sub-meV space-time-energy resolution to the study of material and optical-field dynamics. In addition, these advances enable the manipulation of the wave function of individual free electrons in unprecedented ways, opening sound prospects to probe and control quantum excitations at the nanoscale. Here, we provide an overview of photonics research based on free electrons, supplemented by original theoretical insights and discussion of several stimulating challenges and opportunities. In particular, we show that the excitation probability by a single electron is independent of its wave function, apart from a classical average over the transverse beam density profile, whereas the probability for two or more modulated electrons depends on their relative spatial arrangement, thus reflecting the quantum nature of their interactions. We derive first-principles analytical expressions that embody these results and have general validity for arbitrarily shaped electrons and any type of electron-sample interaction. We conclude with some perspectives on various exciting directions that include disruptive approaches to noninvasive spectroscopy and microscopy, the possibility of sampling the nonlinear optical response at the nanoscale, the manipulation of the density matrices associated with free electrons and optical sample modes, and appealing applications in optical modulation of electron beams, all of which could potentially revolutionize the use of free electrons in photonics.