Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2206.00933 · Physical review. B./Physical review. B

Superbunching in cathodoluminescence: A master equation approach

Tatsuro Yuge, Naoki Yamamoto, Takumi Sannomiya, K. Akiba

Published Apr 6, 2023• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.107.165303

Related papers

Unveiling the nature of cathodoluminescence from photon statistics

Sotatsu Yanagimoto, Naoki Yamamoto, Tatsuro Yuge +2 more

Abstract Cathodoluminescence (CL), the emission of light induced by accelerated free electrons, has been extensively utilized in various applications, such as displays, streak cameras, and high-spatial-resolution analysis of optical materials, surpassing the diffraction limit of light. Despite its long history, the photon statistics of CL have only recently been examined, revealing unexpectedly large bunching of photons. Here we find that this peculiar photon bunching contains information of intervening excitation processes before the photon emission, which can be extracted from the photon statistics within each excitation event by a single free electron. Using this approach, we experimentally unveiled the statistical differences of coherent CL involving a single electromagnetic interaction process and incoherent CL involving multiple excitation processes. The developed formulation is universally applicable for particle generation processes in general to investigate the nature of cascade reactions.

arXiv:2408.12824•Communications Physics•Feb 5, 2025•12 citations

Electron-beam-induced quantum interference effects in a multilevel quantum emitter

H. B. Crispin, Nahid Talebi

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.

arXiv:2501.19230•Physical review. B./Physical review. B•Jun 26, 2025•1 citation

Master-Equation Approach to Spontaneous Emission

G. S. Agarwal

Spontaneous emission from a system of $N$ identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state $|{z}_{0}〉$.

Physical Review A•Nov 1, 1970•232 citations

Superbunching in cathodoluminescence: A master equation approach

NAOKI YAMAMOTO, Takumi Sannomiya

•Apr 1, 2023•0 citations

Measurement of the autocorrelation function of a cathodoluminescence signal: characteristics and applications in nanosecond time resolved and nanometer spatially resolved experiment

Sophie Meuret, Luiz H. G. Tizei, Jean‐Denis Blazit +7 more

In this presentation we show that the autocorrelation function of the cathodoluminescence signal (CL−g(2)(τ)) can be different from the photoluminescence PL−g(2)(τ) showing a huge nanosecond bunching effect g(2)(0) ≫ 1, allowing to retrieve emitters−lifetime at nanometer scale.

•Jan 1, 2014•0 citations

Master-Equation Approach to Spontaneous Emission. II. Emission from a System of Harmonic Oscillators

G. S. Agarwal

In a previous investigation, a general theory for spontaneous emission from a system of $N$ identical atoms or molecules was developed. This theory was based on the master equation recently derived in another paper. In that paper, the master equation relating to spontaneous emission from a system of harmonic oscillators was also derived. In the present investigation, the normally ordered correlation functions for the oscillator system are calculated and these are then used to calculate the radiation-field correlation functions in the far zone. These correlation functions are compared for two different modes of excitation, viz., (i) when each of the oscillators is excited initially to a Fock state, and (ii) when each of the oscillators is excited to some coherent state. It is found that the even-order ($2n$) correlation functions for the second mode of excitation (superradiant excitation) are of order ${N}^{2n}$ higher than those for the first mode of excitation. It is also shown that the photoelectron counting distribution for the superradiant excitation is Poissonian. Finally, the non-Markoffian effects in the spontaneous emission are studied in detail and their connection with exact results is described.

Physical Review A•May 1, 1971•33 citations
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)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ), of this model. We derive the exact formula for the zero-time delay correlation, g(2)(0){g}^{(2)}(0)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)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ), 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.
Abstract Cathodoluminescence (CL), the emission of light induced by accelerated free electrons, has been extensively utilized in various applications, such as displays, streak cameras, and high-spatial-resolution analysis of optical materials, surpassing the diffraction limit of light. Despite its long history, the photon statistics of CL have only recently been examined, revealing unexpectedly large bunching of photons. Here we find that this peculiar photon bunching contains information of intervening excitation processes before the photon emission, which can be extracted from the photon statistics within each excitation event by a single free electron. Using this approach, we experimentally unveiled the statistical differences of coherent CL involving a single electromagnetic interaction process and incoherent CL involving multiple excitation processes. The developed formulation is universally applicable for particle generation processes in general to investigate the nature of cascade reactions.
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.
Spontaneous emission from a system of NNN identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state ∣z0〉|{z}_{0}〉∣z0​〉.
In a previous investigation, a general theory for spontaneous emission from a system of NNN identical atoms or molecules was developed. This theory was based on the master equation recently derived in another paper. In that paper, the master equation relating to spontaneous emission from a system of harmonic oscillators was also derived. In the present investigation, the normally ordered correlation functions for the oscillator system are calculated and these are then used to calculate the radiation-field correlation functions in the far zone. These correlation functions are compared for two different modes of excitation, viz., (i) when each of the oscillators is excited initially to a Fock state, and (ii) when each of the oscillators is excited to some coherent state. It is found that the even-order (2n2n2n) correlation functions for the second mode of excitation (superradiant excitation) are of order N2n{N}^{2n}N2n higher than those for the first mode of excitation. It is also shown that the photoelectron counting distribution for the superradiant excitation is Poissonian. Finally, the non-Markoffian effects in the spontaneous emission are studied in detail and their connection with exact results is described.