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Nanophotonics

Tunable quantum light by modulated free electrons

Valerio Di Giulio, Rudolf Haindl, Claus Ropers

Published May 21, 2025• 6 citations
Publisher

Abstract

Abstract Nonclassical states of light are fundamental in various applications, spanning quantum computation to enhanced sensing. Fast free electrons, which emit light into photonic structures through the mechanism of spontaneous emission, represent a promising platform for generating diverse types of states. Indeed, the intrinsic connection between the input electron wave function and the output light field suggests that electron‐shaping schemes, based on light‐induced scattering, facilitate their synthesis. In this article, we present a theoretical framework capable of predicting the final optical density matrix emitted by a generic N ‐electron state that can also account for post‐sample energy filtering. By using such a framework, we study the modulation‐dependent fluctuations of the N ‐electron emission and identify regions of superradiant scaling characterized by Poissonian and super‐Poissonian statistics. In this context, we predict that high‐ N modulated electron pulses can yield a tenfold shot‐noise suppression in the estimation of the electron‐light coupling when the output radiation intensity is analyzed. In the single‐electron case, we show how coherent states with nearly 90 % purity can be formed by pre‐filtering a portion of the spectrum after modulation, and how non‐Gaussian states are generated after a precise energy measurement. Furthermore, we present a strategy combining a single‐stage electron modulation and post‐filtering to harness tailored light states, such as squeezed vacuum, cat, and triangular cat states, with fidelities close to 100 %.

DOI
10.1515/nanoph-2025-0040

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Tunable quantum light by modulated free electrons

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Abstract Nonclassical states of light are fundamental in various applications, spanning quantum computation to enhanced sensing. Fast free electrons, which emit light into photonic structures through the mechanism of spontaneous emission, represent a promising platform for generating diverse types of states. Indeed, the intrinsic connection between the input electron wave function and the output light field suggests that electron‐shaping schemes, based on light‐induced scattering, facilitate their synthesis. In this article, we present a theoretical framework capable of predicting the final optical density matrix emitted by a generic N ‐electron state that can also account for post‐sample energy filtering. By using such a framework, we study the modulation‐dependent fluctuations of the N ‐electron emission and identify regions of superradiant scaling characterized by Poissonian and super‐Poissonian statistics. In this context, we predict that high‐ N modulated electron pulses can yield a tenfold shot‐noise suppression in the estimation of the electron‐light coupling when the output radiation intensity is analyzed. In the single‐electron case, we show how coherent states with nearly 90 % purity can be formed by pre‐filtering a portion of the spectrum after modulation, and how non‐Gaussian states are generated after a precise energy measurement. Furthermore, we present a strategy combining a single‐stage electron modulation and post‐filtering to harness tailored light states, such as squeezed vacuum, cat, and triangular cat states, with fidelities close to 100 %.
Nonclassical states of light are fundamental in various applications, spanning quantum computation to enhanced sensing. Fast free electrons, which emit light into photonic structures through the mechanism of spontaneous emission, represent a promising platform for generating diverse types of states. Indeed, the intrinsic connection between the input electron wave function and the output light field suggests that electron-shaping schemes, based on light-induced scattering, facilitates their synthesis. In this article, we present a theoretical framework capable of predicting the final optical density matrix of a generic N-electron state that can also account for post-sample energy filtering. By using such framework, we study the modulation-dependent fluctuations of the N-electron emission and identify regions of Poissonian and super-Poissonian statistics. In the single-electron case, we show how coherent states with nearly 90% purity can be formed by pre-filtering a portion of the spectrum after modulation, and how non-Gaussian states are generated after a precise energy measurement. Furthermore, we present a strategy combining a single-stage electron modulation and post-filtering to harness tailored light states, such as squeezed vacuum, cat, and triangular cat states, with fidelity close to 100%.
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.
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.
It has been shown that the spontaneous emission rate of photons by free electrons, unlike stimulated emission, is independent of the shape or modulation of the quantum electron wavefunction (QEW). Nevertheless, here we show that the quantum state of the emitted photons is non-classical and does depend on the QEW shape. This non-classicality originates from the shape dependent off-diagonal terms of the photon density matrix. This is manifested in the Wigner distribution function and would be observable experimentally through homodyne detection techniques as a squeezing effect. Considering a scheme of electrons interaction with a single microcavity mode, we present a QED formulation of spontaneous emission by multiple modulated QEWs through a build-up process. Our findings indicate that in the case of a density modulated QEWs beam, the phase of the off-diagonal terms of the photon state emitted by the modulated QEWs is the harbinger of bunched beam superradiance, where the spontaneous emission is proportional toNe2. This observation offers a potential for enhancement of other quantum electron interactions with quantum systems by a modulated QEWs beam carrying coherence and quantum properties of the modulation.
It has been shown that the spontaneous emission rate of photons by free electrons, unlike stimulated emission, is independent of the shape or modulation of the quantum electron wavefunction (QEW). Nevertheless, here we show that the quantum state of the emitted photons is non-classical and does depend on the QEW shape. This non-classicality originates from the shape dependent off-diagonal terms of the photon density matrix. This is manifested in the Wigner distribution function and would be observable experimentally through Homodyne detection techniques as a squeezing effect. Considering a scheme of electrons interaction with a single microcavity mode, we present a QED formulation of spontaneous emission by multiple modulated QEWs through a build-up process. Our findings indicate that in the case of a density modulated QEWs beam, the phase of the off-diagonal terms of the photon state emitted by the modulated QEWs is the harbinger of bunched beam superradiance, where the spontaneous emission is proportional to N_e^2. This observation offers a potential for enhancement of other quantum electron interactions with quantum systems by a modulated QEWs beam carrying coherence and quantum properties of the modulation.
The pursuit of programmable light sources with high coherence and spectral purity hinges on establishing a precise set of phase relationships in light-matter interactions. Here, we demonstrate that the quadratic dispersion of a freely propagating electron wave packet serves as a programmable quantum medium. Prepared in a coherent momentum-state ladder via a single laser interaction, the electron subsequently undergoes deterministic phase evolution during free propagation-an intrinsic process that compiles its quantum state into two distinct output channels. This mechanism, quantified by a quantum bunching factor, enables (i) Talbot-resonant bunching, where the electron density self-structures into subcycle combs with tunable harmonic selectivity, and (ii) coherent phase transfer of the programmed quadratic phase to light, generating nonclassical photon states such as multicomponent Schrödinger cat states via energy-resolved electron readout. This quadratic-phase programming provides a drift-section platform for Talbot-selected coherent short-wavelength emission and nonclassical light synthesis based on electron self-interference.