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, Marcel Tencé, Mathieu Kociak, Huan‐Cheng Chang, François Treussart, Thomas Auzelle, Karine Hestroffer, B. Daudin
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.
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.
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.
We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale.
Single photon emission is one of the most striking optical properties of semiconductor quantum dots (QDs), and the corresponding photon anti-bunching effect was observed by non-resonant and resonant photoluminescence experiments in single QDs [1,2]. Up to now, all the measurements reported in the literature focus on the incoherent photoluminescence signal for achieving single photon emission. In this regime, the linewidth of the photoluminescence spectrum is limited to the so-called radiative limit. In this paper, we report on the resonant emission (RE) of the exciton in single InAs/GaAs QDs embedded in a planar microcavity [2]. We present an original type of single photon source based on the coherent laser light scattering by a single QD [3]. Besides the antibunching effect showing the nonclassical nature of the emitted light, we observe that the QD emission spectrum is determined by the spectrum of the resonant excitation laser. Figure (a,b,c) shows high-resolution measurements by Fourier transform spectroscopy of the RE where the data are fitted to the first-order correlation function g(1)(τ) of the RE of a two-level system. The inverse Fourier transform of the g(1)(τ) function allows a direct comparison of the different RE emission profiles in figure (d,e,f). By reducing the resonant excitation power, the Mollow triplet shrinks to a single narrow Lorentzian line, while the relative intensity of this narrow peak increases and tends to overwhelm the RE spectrum. This implies that single QDs can produce single photons with a coherence time that is not limited anymore by the QD electronic properties, resulting in an ultra-coherent character [3]. References [1] P. Michler et al, Science 290, 2282 (2000). [2] H. S. Nguyen et al, Phys. Rev. Lett. (accepted, in press). See arXiv 1109.4304. [3] H. S. Nguyen et al, Appl. Phys. Lett. 99, 261904 (2011).
Quantum optics performed at the nanometer scale is an important challenge, especially for quantum emitters characterization. They can be point defects in material (few ang- ströms) or confined structures of a few nanometers. A way to reach this scale is by using cathodoluminescence (CL) performed in a scanning transmission electron microscope (CL- STEM), which has only recently been done [1]. However, when aiming at studying the statistical properties of the light coming out of a CL experiment, which is necessary to e. g. study the quantum nature of Single Photon Emitters (SPE) emission, dedicated expe- riments on top of regular CL ones have to be designed. Few months before my arrival in the STEM-group of the LPS, an intensity interferometry experiment (HBT) that measures the autocorrelation function g(2) of the CL signal intensity was built [2]. It is well known that the clear signature of SPE as measured in photoluminescence (PL) is antibunching in the g(2)(τ), namely that the autocorrelation function is always less than one. It was re- cently demonstrated on a famous SPE, the Nitrogen vacancy (NV) defect in diamond, that CL-STEM is similar to PL when only one SPE is involved. In this thesis we will see how CL-STEM allowed to characterize a new point defect in h-BN, showing the relevance of HBT experiments in a CL-STEM for discovering and characterizing new SPE. However, by studying the excitation of multiple SPE in CL, we discovered a new emission phenomenon, characterized by a huge bunching effect of the g(2)(τ) function (g(2)(0) > 35), in complete contradiction to PL measurements and expectations (g(2)(0)<1). In my thesis manuscript, this surprising effect will be experimentally investigated, theoretically explained and applied to lifetime measurement at the nanometer scale. Because quantum optics is often linked to quantum plasmonics, I will present, to conclude, a theoretical proposal, in collaboration with J. Garcia de Abajo, about quantum plasmonics measurement in a STEM.