The statistics of photons emitted by single multilevel systems is investigated with emphasis on the nonrenewal characteristics of the photon-arrival times. We consider the correlation between consecutive interphoton times and present closed-form expressions for the corresponding multiple-moment analysis. Based on the moments, a memory measure is proposed which provides an easy way of gauging the nonrenewal statistics. Monte Carlo simulations demonstrate that the experimental verification of nonrenewal statistics is feasible.
The statistics of photons emitted by single multilevel systems is investigated with emphasis on the nonrenewal characteristics of the photon-arrival times. We consider the correlation between consecutive interphoton times and present closed-form expressions for the corresponding multiple-moment analysis. Based on the moments, a memory measure is proposed which provides an easy way of gauging the nonrenewal statistics. Monte Carlo simulations demonstrate that the experimental verification of nonrenewal statistics is feasible.
Photon statistics is a branch of physics that involves observing the behavior of single or a small number of photons and then aggregating the results through statistical averaging. This process is essential to obtain meaningful and reliable data, especially in quantum optics research. Photon statistics provides valuable information about correlations in the electromagnetic field and characteristics of the type of light being measured. For example, second-order correlation function obtained via Hanbury Brown and Twiss experiment is the fundamental way to differentiate between coherent, chaotic and quantum light. Moreover, extensive investigations into the quantum properties of light resulted in significant progress that allows for precise control of quantum optical systems and sets the stage for genuine quantum engineering. This progress extends to applications in confirming the generation of entangled photons and exploring their properties for various purposes. The non-classical correlation between the entangled photons has resulted in various quantum optical techniques that enable the practical implementation of conceptual experiments that probe the core principles of quantum theory. This enhanced control over quantum phenomena offers exciting opportunities to explore novel information-processing approaches, with the potential to revolutionize technologies rooted in quantum information science. Driven by the significance and pivotal role of photon statistics, our research pursuits were directed toward two specific domains: the characterization of nanolasers and the characterization of time-bin entangled photons. In the first segment, we delve into the realm of metallic coaxial nanolasers, renowned for their intriguing threshold-less lasing behavior. Through comprehensive photon statistics analysis, we seek to unravel the coherence properties inherent in these nanolasers. Our focus also lies on understanding the elusive threshold-less operation, which has remained a subject of debate and intrigue. To evaluate this unique lasing characteristic, we conduct rigorous second-order coherence measurements alongside time-resolved second-order correlation analyses. The second segment of this study ventures into the generation and characterization of high-dimensional time-bin entangled states, a critical resource for quantum technological applications. We simulate a synthetic photonic lattice by employing a coupled fiber-loop system to perform various quantum walk schemes to generate and process high-dimensional time-bin entangled states. Our investigation focuses on the quantum interference phenomena through detailed photon statistics analysis, with an emphasis on their applications across diverse quantum technologies. Through these two interconnected research endeavors, this thesis demonstrates the profound significance of photon statistics as a versatile tool, bridging classical and quantum realms, and paving the way for advancements in diverse applications, ranging from nanolasers to quantum technologies.
We study the general properties of the photon statistics of fluorescence radiation, emitted by a two-level atom in a strong laser field and a perturber bath. We investigate the deviation of the factorial moments from a Poisson distribution, and we show that for long counting times the lowest-order correction can be expressed entirely by the quantity Q, which represents the deviation of the variance from the average. We introduce and evaluate the quantities gn(t), which serve as a measure for the deviation of the higher-order statistics from Poissonian statistics. Subsequently we obtain explicit expressions for the average waiting time for the appearance of the n th photon, after an arbitrary initialization of the counting process. It turns out that the average time delay is again determined by Q. Hence this parameter can be measured in a photon-counting experiment, which involves only the observation of a single photon, rather than an (in principle) infinite number of photons.
This thesis intends to familiarize the reader with the concepts of photon statistics and correlations in quantum optics. Developing light sources that emit quantum states is central for the realization of quantum technologies. One important step in characterizing these sources is the measurement of field fluctuations and correlations, by coincidence measurements. The expectation value of a coincidence measurement, a simultaneous measurement of two intensities (or, more general, four fields), is represented by the fourth-order correlation function. The value of the correlation function, at zero delay between the detection of two photons, reveals important properties of the state to which they belonged, for example the fluctuations of the photon number. Since predictability is important for many applications, light sources emitting single photons are also characterized by the indistinguishability of consecutively emitted photons, or of two photons from separate emitters. In paper I we investigate blinking behaviour in quantum emitters, and its effect on the interference pattern and photon statistics with photons from two separate emitters. Blinking refers to an emitters transition into a non-emitting state, and subsequent transition back to an emitting state. We show that blinking can not be treated as linear loss, when measuring the fourth-order correlation function for two emitters in a Hong-Ou-Mandel setup. In general, a measurement of the fourth-order correlation function is robust to loss, which makes it a very practical tool. However, the relation between recorded coincidence counts and the correlation function is only direct in the limit of zero detection efficiency, and depends on the detection system. In paper II, we show that by adding a variable attenuation in the beam path, we can trace back to the ''true'' value of the correlation function at zero quantum efficiency. This method improves accuracy in correlation measurements by decreasing a systematic error at the expense of an increased statistical error, which is easier to handle, extending the use of coincidence methods to classical and non-classical multi-photon states.
Abstract Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.
The formation of protein complexes with other proteins and nucleic acids is critical to biological function. Although it is relatively easy to identify the components present in these complexes, it is often difficult to determine their exact stoichiometry and obtain information about the homogeneity of the sample from bulk measurements. We demonstrate the use of single molecule photon-pair correlation spectroscopy to distinguish between discrete numbers of molecules in biological complexes. Fluorescence photon antibunching is observed from a single molecule by employing time-correlated single photon counting in combination with a Hanbury-Brown and Twiss coincidence setup. In addition, pulsed laser excitation and time-tagged time-resolved data collection allow for the measurement of photon arrival times with nanosecond time resolution. The interphoton time distribution between consecutively arriving photons can be calculated and provides a measure of the second-order temporal correlation function. Analysis of this function yields an absolute measure of the number of molecules, N, present in a given complex. It is this ability to measure N that renders this technique powerful for determining stoichiometries in complex biological systems at the single molecule level. We investigate the counting efficiency and statistics of photon antibunching of specifically designed biological samples labeled with multiple copies of the same fluorescent dye and derive conclusions about its use in the analytical evaluation of complex biological samples.