Controlling and generating ultrafast free-electron wavepackets via laser is pivotal for photon-induced near-field electron microscopes (PINEM) and also for developing compact, coherent free-electron radiation sources. Here, we present a quantum echo-enabled high-harmonic generation (QEEHG) scheme that manipulates the quantum phase of electron wavepackets to produce tunable, coherent high-harmonic radiation at ultrashort wavelengths. This framework, inspired by the EEHG concept for free-electron lasers by Stupikov et al. (2009), leverages multiphoton PINEM scattering followed by dispersive chirp sections to induce quantum interference among photon sidebands. Such interference selectively enhances a targeted harmonic order - for instance, the 60th harmonic at 13.3nm from an 800nm seeding - while suppressing unwanted radiations. The optimization of harmonic orders and its non-classical spectral characteristics are analyzed. This quantum echo technique establishes a promising paradigm for compact coherent sources and provides new perspectives for quantum wavefunction shaping in ultrafast electron microscopy and diffraction.
Controlling and generating ultrafast free-electron wavepackets via laser is pivotal for photon-induced near-field electron microscopes (PINEM) and also for developing compact, coherent free-electron radiation sources. Here, we present a quantum echo-enabled high-harmonic generation (QEEHG) scheme that manipulates the quantum phase of electron wavepackets to produce tunable, coherent high-harmonic radiation at ultrashort wavelengths. This framework, inspired by the EEHG concept for free-electron lasers by Stupikov et al. (2009), leverages multiphoton PINEM scattering followed by dispersive chirp sections to induce quantum interference among photon sidebands. Such interference selectively enhances a targeted harmonic order - for instance, the 60th harmonic at 13.3nm from an 800nm seeding - while suppressing unwanted radiations. The optimization of harmonic orders and its non-classical spectral characteristics are analyzed. This quantum echo technique establishes a promising paradigm for compact coherent sources and provides new perspectives for quantum wavefunction shaping in ultrafast electron microscopy and diffraction.
Coherent optical modulation of free-electron wavepackets offers a route to ultrafast beam steering, energy exchange, temporal compression, and quantum-state shaping. Recent advances in photon-induced near-field electron microscopy (PINEM), ultrafast Kapitza-Dirac effect (KDE) and dielectric laser acceleration (DLA) have demonstrated strong light-electron coupling, but longitudinal energy modulation, transverse momentum transfer, and wavepacket-dependent diffraction are still commonly described with separate models. Here, we develop a unified Light-Electron Modulation (LEM) framework that treats optical near fields as programmable phase modulators for free-electron wavepackets. Within this framework, we identify longitudinal and transverse modulation channels, analogous to electro-optic phase modulation and acousto-optic diffraction of light, respectively, and show how their operation depends on wavepacket extent, recoil, phase matching, and optical-field geometry. This formulation organizes PINEM, Raman-Nath and Bragg diffraction, DLA-like acceleration, and anomalous PINEM as limiting regimes of a common modulation picture. The resulting framework provides design principles for free-electron modulators that can control energy spectra, temporal density, transverse wavefronts, and electron-photon quantum interfaces, establishing LEM as a device-level platform for programmable femtosecond-to-attosecond matter-wave control.
The generation and control of extreme ultraviolet (XUV) radiation by high harmonic generation (HHG) have advanced ultrafast science, providing direct insights into electron dynamics on their natural time scale. Attosecond science has established the capability to resolve ultrafast quantum phenomena in matter by characterizing and controlling the classical properties of the high harmonics. Recent theoretical proposals have introduced novel schemes for generating and manipulating XUV HHG with distinct quantum features, paving the way to attosecond quantum optics. In this work, we transfer fundamental concepts in quantum optics into attosecond science. By driving the HHG process with a combination of an infrared bright squeezed vacuum (BSV, a non-classical state of light), and a strong coherent field, we imprint the quantum correlations of the input BSV onto both the ultrafast electron wavefunction and the harmonics' field. Performing in-situ HHG interferometry provides an insight into the underlying sub-cycle dynamics, revealing squeezing in the statistical properties of one of the most fundamental strong-field phenomena -- field induced tunneling. Our measurement allows the reconstruction of the quantum state of the harmonics through homodyne-like tomography, resolving correlated fluctuations in the harmonic field that mirror those of the input BSV. By controlling the delay between the two driving fields, we manipulate the photon statistics of the emitted attosecond pulses with sub-cycle accuracy. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.
The coherent interaction between free electrons and optical near-fields enables the active modulation of electron wave packets, a mechanism central to photon-induced near-field electron microscopy (PINEM). While existing theories effectively describe these interactions at high kinetic energies, the growing interest in low-energy ultrafast electron microscopy demands frameworks that explicitly account for finite wave packet geometries and recoil effects. In this paper, we develop a rigorous 3D quantum scattering theory for electron wave packets interacting with time-periodic potentials, capturing the case of optical near-field interaction. By mapping the time-dependent dynamics into an extended Floquet space, we formally connect the modulation process to time-independent multi-channel scattering. We evaluate the resulting scattering amplitudes using both an exact R-matrix approach and a multi-channel eikonal approximation. The latter analytical approach recovers PINEM-like probabilities weighted by the wave packet's transverse profile. Application of the theory to an oscillating potential demonstrates the generation of distinct energy sidebands, revealing that the modulation strength is sensitive to the transverse focusing of the incident electron pulse, underlining the importance of a fully 3D treatment.
Since the birth of quantum optics, the measurement of quantum states of nonclassical light has been of tremendous importance for advancement in the field. To date, conventional detectors such as photomultipliers, avalanche photodiodes, and superconducting nanowires, all rely at their core on linear excitation of bound electrons with light, posing fundamental restrictions on the detection. In contrast, the interaction of free electrons with light in the context of quantum optics is highly nonlinear and offers exciting possibilities. The first experiments that promoted this direction appeared over the past decade as part of photon-induced nearfield electron microscopy (PINEM), wherein free electrons are capable of high-order multi-photon absorption and emission. Here we propose using free electrons for quantum-optical detection of the complete quantum state of light. We show how the precise control of the electron before and after its interaction with quantum light enables to extract the photon statistics and implement full quantum state tomography using PINEM. This technique can reach sub-attosecond time resolutions, measure temporal coherence of any degree (e.g., g(1), g(2)), and simultaneously detect large numbers of photons with each electron. Importantly, the interaction of the electron with light is non-destructive, thereby leaving the photonic state (modified by the interaction) intact, which is conceptually different from conventional detectors. By using a pulse of multiple electrons, we envision how PINEM quantum detectors could achieve a single-shot measurement of the complete state of quantum light, even for non-reproducible emission events. Altogether, our work paves the way to novel kinds of photodetectors that utilize the ultrafast duration, high nonlinearity, and non-destructive nature of electron-light interactions.
Quantum high-harmonic generation (HHG) is a prominent and growing field of research with potential capabilities of providing high photon-number entangled states of light. However, there is an open debate regarding the theory level required for correctly describing the quantum aspects of HHG, such as squeezing or entanglement. Previous approaches either semi-classically sampled the quantum electromagnetic field distribution, or employed perturbation theory utilizing the semi-classical simulations as a starting point. Both of these schemes miss out key quantum-optical features as self-consistent numerical simulations of the electron-photon wavefunction are not performed at any stage. In this Letter, we develop a full quantum theory for multipartite entanglement in HHG, solving exactly the light-matter interaction Hamiltonian in a given Hilbert space, and employ it for evaluating the quantum correlations of emitted photons. We show that HHG entanglement oscillates with the driving laser power and exhibits multiple local maxima, which allows fine-tuning HHG entanglement. Such features arise for both above-threshold harmonics and between above- and below-threshold harmonics. By analyzing different types of atomic targets, we find that the long-range behavior of driven electrons can qualitatively change the resulting entanglement, potentially leading to non-universal behavior across systems. Lastly, we show that focal averaging over classical degrees of freedom in fact plays a key role in entanglement measures and can change the qualitative behavior of observables. Our work establishes the state-of-the art in exploring entanglement features in HHG, and paves way for analysis and engineering of entangled multi-photon states in the XUV and ultrafast regime for more complex matter systems.
Ultrafast high harmonic beams provide new opportunities for coherently controlling excitation and ionization processes in atoms, molecules, and materials on attosecond time scales by employing multiphoton two-pathway electron-wave-packet quantum interferences. Here we use spectrally tailored and frequency tuned vacuum and extreme ultraviolet harmonic combs, together with two phase-locked infrared laser fields, to show how the total single and double photoionization yields of argon can be coherently modulated by controlling the relative phases of both optical and electronic-wave-packet quantum interferences. This Letter is the first to apply quantum control techniques to double photoionization, which is a fundamental process where a single, high-energy photon ionizes two electrons simultaneously from an atom.