We study the quantum interaction between free electrons and photons in a time-varying media, and find that periodic modulation exponentially amplifies electron-photon coupling within momentum gaps, enabling arbitrarily large momentum transfer. By preparing the light in a two-mode squeezed vacuum state, the electron momentum grows faster than its spectral spreading, establishing time-modulated photonic media as a platform for accelerating free-electrons and shaping their quantum state.
We study the quantum interaction between free electrons and photons in a time-varying media, and find that periodic modulation exponentially amplifies electron-photon coupling within momentum gaps, enabling arbitrarily large momentum transfer. By preparing the light in a two-mode squeezed vacuum state, the electron momentum grows faster than its spectral spreading, establishing time-modulated photonic media as a platform for accelerating free-electrons and shaping their quantum state.
Photonic time crystals host a variety of intriguing phenomena, from wave amplification and mixing to exotic band structures, all stemming from the time-periodic modulation of optical properties. While these features have been well described classically, their quantum manifestation when coupled to an atomic electric dipole has remained elusive. Here, we introduce a quantum electrodynamical model of photonic time crystals that reveals a deeper connection between classical and quantum pictures: the classical momentum gap arises from a localization-delocalization quantum phase transition in a Floquet-photonic synthetic lattice. Leveraging an effective Hamiltonian perspective, we pinpoint the critical momenta and highlight how classical exponential field growth manifests itself as wave-packet acceleration in the quantum synthetic space. Remarkably, when a two-level atom is embedded in such a photonic time crystal, its Rabi oscillations undergo irreversible decay to a half-and-half mixed state-a previously unobserved phenomenon driven by photonic delocalization within the momentum gap, even with just a single frequency mode. Our findings establish photonic time crystals as versatile platforms for studying nonequilibrium quantum photonics and suggest new avenues for controlling light matter interactions through time domain engineering.
Optical parametric processes underpin quantum photonics, while free-electron--photon interactions offer agile pathways to generate nontrivial quantum photonic states. These threads have so far largely progressed independently, whereas placing free electrons in a driven nonlinear system can potentially activate coherent parametric interaction channels for joint state engineering of both types of particles. Here we unify these paradigms by developing a general theoretical framework for parametric free-electron--photon interactions in a nonlinear optical system driven by degenerate parametric down-conversion. Unlike free electrons in a linear bath, here they can couple to Bogoliubov quasiparticles through two detuned phase-matching channels, where the parametric process and free-electron interactions can quantum amplify each other. Seeding the interaction with squeezed vacuum yields gain-only or loss-only electron energy spectra, and enables electron-heralded squeezed Fock states; with bare vacuum, postselecting electron energy sidebands generates high-fidelity Schrödinger cat states. Our results show how optical parametric interactions can quantum shape free electrons and photons, potentially enabling a quantum parametric dielectric laser accelerator that mitigates the need for temporal phase synchronization, thereby allowing acceleration probabilities to approach unity even for phase-random electrons.
Over the last few decades, the predominant strategies for controlling spontaneous emission have involved tailoring the spatial surroundings of quantum emitters or atoms to create resonant or spatially periodic photonic structures. However, the rise of time-varying photonics has prompted a reevaluation of spontaneous emission in dynamically changing environments, especially within photonic time crystals, where optical properties undergo time-periodic modulation. Here, we apply classical light-matter interaction theory together with Floquet analysis to reveal a substantial enhancement of the spontaneous emission decay rate at the momentum gap frequency in photonic time crystals. Moreover, our findings suggest that photonic time crystals enable a nonequilibrium light-matter interaction process: the spontaneous excitation of an atom from its ground state to an excited state, accompanied by the concurrent emission of a photon, referred to as spontaneous emission excitation.
It is a long-standing goal to create light with unique quantum properties such as squeezing and entanglement. We propose the generation of quantum light using free-electron interactions, going beyond their already ubiquitous use in generating classical light. This concept is motivated by developments in electron microscopy, which recently demonstrated quantum free-electron interactions with light in photonic cavities. Such electron microscopes provide platforms for shaping quantum states of light through a judicious choice of the input light and electron states. Specifically, we show how electron energy combs implement photon displacement operations, creating displaced-Fock and displaced-squeezed states. We develop the theory for consecutive electron-cavity interactions with a common cavity and show how to generate any target Fock state. Looking forward, exploiting the degrees of freedom of electrons, light, and their interaction may achieve complete control over the quantum state of the generated light, leading to novel light statistics and correlations.
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-TM 00 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.
Light is used to steer the motion of atoms in free space, enabling cooling and trapping of matter waves through ponderomotive forces and Doppler-mediated photon scattering. Likewise, light interaction with free electrons has recently emerged as a versatile approach to modulate the electron wave function for applications in ultrafast electron microscopy. Here, we combine these two worlds, theoretically demonstrating that matter waves can be optically manipulated via inelastic interactions with optical fields. This allows us to modulate the translational part of the wave function and produce temporally and spatially compressed atomic beam pulses. We realize such modulation through stimulated photon absorption and emission by atoms traversing phase-matching evanescent optical fields generated upon light scattering by a nanostructure and via stimulated Compton scattering in free space without any assistance from material media. Our results support optical manipulation of matter waves as a powerful tool for microscopy, spectroscopy, and exploration of fundamental phenomena associated with light-atom interactions.