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 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.
Do the prior history and the wave-packet size and form of a free electron have a physical effect in its interaction with light? Here we answer these fundamental questions on the interpretation of the electron quantum wave function by analyzing spontaneous and stimulated emissions of a quantum electron wave packet, interacting with a general, quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission and absorption of photons depends on the preinteraction-history-dependent size, exhibiting spectral cutoff when it exceeds the interacting radiation wavelength. Furthermore, stimulated emission of an optically modulated electron wave packet has a characteristic harmonic emission spectrum beyond the cutoff, which depends on the modulation features. In either case, there is no wave-packet-dependent radiation of the Fock state, and particularly the vacuum state spontaneous emission is wave-packet independent. The classical-to-quantum transition of radiation from the point-particle to the plane-wave limits, and the effects of wave-packet modulation indicate a way of measuring the wave-packet size of a single electron wave function, and suggest an alternative direction for exploring light-matter interaction.
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%.
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 %.
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.
We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.