Multiphoton correlations and emitters

A thesis submitted in partial fulfilment of the requirements of the University of Wolverhampton for the degree of Doctor of Philosophy.The characterisation of the quantum states of light and their subsequent realisation is thought to be an indispensable step to bring in quantum technologies to the real world. The emergence of quantum cryptography, quantum security protocols or quantum computers, among others, demand implicitly or explicitly trustworthy tools and components to carry through the research in its first stages. A deterministic or on-demand single-photon source and, more recently, an N-photon emitter, seem to play a crucial role. Nevertheless, even the correct characterisation of the former is still a source of discussion and there exist several criteria to do so. The identification of the latter is, as expected, a challenging task. With the emergence of multiphoton physics, the horizon of quantum light sources is wider. The tools to identify and classify multiphoton emission are still in development. We present the methods to study the dynamics and correlations of some candidate systems that have been proposed, focusing on the analytical solutions through perturbative methods, valid, for instance, for weakly driven or weakly coupled systems. In particular, the frequency-resolved correlations can be exactly obtained in this way. We also consider the effect of detection on the correlations. The noisy apparatus and their finite time resolution can modify the photon statistics. Some photons may be left undetected or misplaced (in time), additional counts may be recorded as well. We revisit the photon counting formula, that was popular in the birth of Quantum Optics, to obtain the counting probabilities in continuously driven (CW) systems and we focus then on the spontaneous emission of N photons. We observe, for probability distributions of CW systems, a clear deviation from Poissonian statistics in both the short and long time regimes. We find how such a behaviour is inherited from the photon correlations. A good starting point to study the bundler—the N-photon emitter—is the spontaneous emission of N photons. The counting probabilities are computed without and with spectral filtering, making emphasis on how the kind of filter affects the detection. Then, the full structure of the bundle is completely captured by the probability functions of the emission time of the individual photons. The results are ultimately compared with the actual bundler, showing qualitative and quantitative agreement. A brief introduction is given to spatial correlation induced by the ensemble statistics. Some clarifying examples reveal how the statistics are manifested depending on the kind of states. On the other hand, a dynamical model introducing a space dependent sensor method is provided for the scattering and how the spatial distribution is modified by the time resolution limitation. Interestingly, the wave packet before and after the scattering get effectively admixed and interfere with itself displaying characteristic fringes. The main objective of this Thesis is to make an exhaustive characterisation of multiphoton emission, starting with the usual treatment in terms of the luminescence spectrum and the second-order photon correlation function g(2), considering mechanisms that can take place in the detection process such as spectral filtering or contamination of the signal due to time jitter and noise. We develop tools to facilitate and speed up the computation of these quantities, either analytically or numerically, within the range of validity of the Born–Markov approximation and highlighting situations in which perturbation theory is applicable. Finally, we go beyond and take into account other statistical quantities such as the waiting time distribution or higher order correlators and eventually compute counting statistics, which results in a good and promising procedure to characterise and subsequently classify multiphoton emission

Two-photon emission in detuned resonance fluorescence

We discuss two-photon correlations from the side peaks that are formed when a two-level system emitter is driven coherently, with a detuning between the driving source and the emitter (quasi-resonance fluorescence). We do so in the context of the theories of frequency-resolved photon correlations and homodyning, showing that their combination leads to a neat picture compatible with perturbative two-photon scattering that was popular in the early days of quantum electrodynamics. This should help to control, enhance and open new regimes of multiphoton emission. We also propose a way to evidence the quantum coherent nature of the process from photoluminescence only, through the observation of a collapse of the symmetry of the lineshape accompanied by a surge of its intensity of emission. We discuss several of our results in the light of recent experimental works.Comment: 17 pages, 4 figures -- added ideal two-photon cascade formula (Eq. 3), additional references, corrected some typos & other minor changes. Submitted to Quantum Sci. Techno

Loss of antibunching

We describe some of the main external mechanisms that lead to a loss of antibunching, i.e., that spoil the character of a given quantum light to deliver its photons separated from each other. Namely, we consider contamination by noise, a time jitter in the photon detection, and the effect of frequency filtering (or detection with finite bandwidth). The formalism to describe time jitter is derived and connected to the already existing one for frequency filtering. The emission from a two-level system under both incoherent and coherent driving is taken as a particular case of special interest. The coherent case is further separated into its vanishing- (Heitler) and high- (Mollow) driving regimes. We provide analytical solutions which, in the case of filtering, reveal an unsuspected structure in the transitions from perfect antibunching to thermal (incoherent case) or uncorrelated (coherent case) emission. The experimental observations of these basic and fundamental transitions would provide additional compelling evidence of the correctness and importance of the theory of frequency-resolved photon correlation

The Origin of Antibunching in Resonance Fluorescence

Epitaxial quantum dots have emerged as one of the best single-photon sources, not only for applications in photonic quantum technologies but also for testing fundamental properties of quantum optics. One intriguing observation in this area is the scattering of photons with subnatural linewidth from a two-level system under resonant continuous wave excitation. In particular, an open question is whether these subnatural linewidth photons exhibit simultaneously antibunching as an evidence of single-photon emission. Here, we demonstrate that this simultaneous observation of subnatural linewidth and antibunching is not possible with simple resonant excitation. First, we independently confirm single-photon character and subnatural linewidth by demonstrating antibunching in a Hanbury Brown and Twiss type setup and using high-resolution spectroscopy, respectively. However, when filtering the coherently scattered photons with filter bandwidths on the order of the homogeneous linewidth of the excited state of the two-level system, the antibunching dip vanishes in the correlation measurement. Our experimental work is consistent with recent theoretical findings, that explain antibunching from photon-interferences between the coherent scattering and a weak incoherent signal in a skewed squeezed state.Comment: 8 pages, 4 figure

Origin of antibunching in resonance fluorescence

Resonance fluorescence has played a major role in quantum optics with predictions and later experimental confirmation of nonclassical features of its emitted light such as antibunching or squeezing. In the Rayleigh regime where most of the light originates from the scattering of photons with subnatural linewidth, antibunching would appear to coexist with sharp spectral lines. Here, we demonstrate that this simultaneous observation of subnatural linewidth and antibunching is not possible with simple resonant excitation. Using an epitaxial quantum dot for the two-level system, we independently confirm the single-photon character and subnatural linewidth by demonstrating antibunching in a Hanbury Brown and Twiss type setup and using high-resolution spectroscopy, respectively. However, when filtering the coherently scattered photons with filter bandwidths on the order of the homogeneous linewidth of the excited state of the two-level system, the antibunching dip vanishes in the correlation measurement. Our observation is explained by antibunching originating from photon-interferences between the coherent scattering and a weak incoherent signal in a skewed squeezed state. This prefigures schemes to achieve simultaneous subnatural linewidth and antibunched emissio

Luz cuántica con campos clásicos

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica de la Materia Condensada. Fecha de Lectura: 18-04-202

Tuning photon statistics with coherent fields

Photon correlations, as measured by Glauber's $n$-th order coherence functions $g^{(n)}$, are highly sought to be minimized and/or maximized. In systems that are coherently driven, so-called blockades can give rise to strong correlations according to two scenarios based on level-repulsion (conventional blockade) or interferences (unconventional blockade). Here we show how these two approaches relate to the admixing of a coherent state with a quantum state such as a squeezed state for the simplest and most recurrent case. The emission from a variety of systems, such as resonance fluorescence, the Jaynes-Cummings model or microcavity polaritons, as a few examples of a large family of quantum optical sources, are shown to be particular cases of such admixtures, that can further be doctored-up externally by adding an amplitude- and phase-controlled coherent field with the effect of tuning the photon statistics from exactly zero to infinity. We show how such an understanding also allows to classify photon statistics throughout platforms according to conventional and unconventional features, with the effect of optimizing the correlations and with possible spectroscopic applications. In particular, we show how configurations that can realize simultaneously conventional and unconventional antibunching bring the best of both worlds: huge antibunching (unconventional) with large populations and being robust to dephasing (conventional).Comment: Published versio