Cathodoluminescence spectroscopy has recently emerged as a novel platform for nanoscale control of nonclassical features of light. Here, we propose a theoretical model for cathodoluminescence from a multilevel quantum emitter. Employing a master equation approach and treating the electron-beam excitation as an incoherent broadband field source, we show that quantum interference can arise between the different relaxation pathways. The induced interference can significantly modify the time-dependent spectra resulting in the enhancement or suppression of cathodoluminescence. We find that the excitation rate, initial state of the emitter, and excited level spacing play a crucial role in determining the influence of interference. Our findings shed light on electron-beam-induced quantum interference in cathodoluminescence and provides a theoretical basis for exploring quantum optical phenomena in electron-driven multilevel systems.
Cathodoluminescence spectroscopy has recently emerged as a novel platform for nanoscale control of nonclassical features of light. Here, we propose a theoretical model for cathodoluminescence from a multilevel quantum emitter. Employing a master equation approach and treating the electron-beam excitation as an incoherent broadband field source, we show that quantum interference can arise between the different relaxation pathways. The induced interference can significantly modify the time-dependent spectra resulting in the enhancement or suppression of cathodoluminescence. We find that the excitation rate, initial state of the emitter, and excited level spacing play a crucial role in determining the influence of interference. Our findings shed light on electron-beam-induced quantum interference in cathodoluminescence and provides a theoretical basis for exploring quantum optical phenomena in electron-driven multilevel systems.
The resonant quantum dynamics of an excited two-level emitter is investigated via classical modulation of its transition frequency while simultaneously the radiator interacts with a broadband electromagnetic field reservoir. The frequency of modulation is selected to be of the order of the bare-state spontaneous decay rate. In this way, one can induce quantum interference effects, and consequently, quantum coherences among multiple decaying transition pathways. Depending on the modulation depth and its absolute phase, both the spontaneous emission and the frequency shift may be conveniently modified and controlled.
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.
Electron--photon quantum entanglement in an electron microscope paves the way for a new quantum platform, enabling the integration of quantum functionalities into electron microscopy and opening opportunities for quantum imaging and quantum sensing at the nanoscale. To realize such a platform, it is crucial to understand the degree and nature of electron--photon entanglement in cathodoluminescence (CL). However, its dependence on electron-beam properties, particularly transverse coherence, remains unclear. Here, we present a theoretical framework describing the quantum state of an electron--photon pair generated in coherent CL from a system with translational invariance in the plane perpendicular to the electron beam, as can be realized, for example, in transition radiation at a planar interface. By expressing the scattered state directly in terms of the luminescence spectrum, we evaluate the entanglement using both subsystem purity and an Einstein--Podolsky--Rosen-type criterion. These two measures enable a clear distinction among wave-like, particle-like, and classical regimes in terms of spatial and momentum entanglement in the electron--photon system. Our analysis identifies the roles of the electron's transverse and longitudinal coherence, as well as the photon's spectral width, and reveals the conditions under which strong spatial entanglement emerges. This unified perspective clarifies the nature of electron--photon quantum correlations in coherent CL and advances the development of quantum-enabled functionalities in electron microscopy.
Abstract Quantum coherence and interference offer novel pathways to control light–matter interaction at the atomic scale, with enticing prospects in both fundamental and applied science. Here, we demonstrate coherent control over transient excitation of localized surface plasmon modes of a silver nanosphere adjacent to a quantum coherence medium composed of three-level quantum emitters, using a theoretical approach. We show that quantum interference enables more than two orders of magnitude enhancement in the surface plasmon field generated when the quantum emitters are driven coherently, in comparison to incoherent pumping. Furthermore, under optimal conditions, intense surface plasmon lasing can be induced without population inversion on the spasing transition. Our results open up the possibility of overcoming dissipative losses in plasmonic modes in the transient regime when steady-state population inversion is difficult to achieve due to fast relaxation rates and impractical pumping requirements.
Recent advances in time-resolved cathodoluminescence have enabled ultrafast studies of single emitters in quantum materials with femtosecond temporal resolution. Here, we develop a quantum theory modeling the dynamics of free electrons interacting with quantum emitters in arbitrary initial states. Our analysis reveals that a free electron can induce transient coherent oscillations in the populations when the system is initially prepared in a coherent superposition of its states. Moreover, the electron energy spectrum exhibits a clear signature of the quantum coherence and sensitivity to the transition frequency of the emitter. These coherence effects manifest themselves as oscillations in the zero-loss peak of the spectral energy-loss probability. Our findings pave the way for characterization of quantum-coherent dynamics of individual quantum emitters by electron-probes.
We propose a theoretical model of a master equation for cathodoluminescence (CL). The master equation describes simultaneous excitation of multiple emitters by an incoming electron and radiative decay of individual emitters. We investigate the normalized second-order correlation function, ${g}^{(2)}(\ensuremath{\tau})$, of this model. We derive the exact formula for the zero-time delay correlation, g(2)(0), and show that the model successfully describes giant bunching (superbunching) in the CL. We also derive an approximate form of ${g}^{(2)}(\ensuremath{\tau})$, which is valid for small excitation rate. Furthermore, we discuss the state of the radiation field of the CL. We reveal that the superbunching results from a mixture of an excited photon state and the vacuum state and that this type of state is realized in the CL.