Exciting with quantum light

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica de la Materia Condensada. Fecha de lectura: 22-11-2019A two-level system—the idealization of an atom with only two energy levels—is the most fundamental quantum object. As such, it has long been at the forefront of the research in Quantum Optics: its emission spectrum is simply a Lorentzian distribution, and the light it produces is the most quantum that can be. The temporal distribution of the photon emission displays a perfect antibunching, meaning that such a system will never emit two (or more) photons simultaneously, which is consistent with the intuition that the two-level system can only sustain a single excitation at any given time. Although these two properties have been known for decades, it was not until the advent of the Theory of Frequency-filtered and Time-resolved Correlations that it was observed that the perfect antibunching is not the end of the story: the correlations between photons possess an underlying structure, which is unveiled when one retains the information about the color of the photons. This is a consequence of the Heisenberg uncertainty principle: measuring perfect antibunching implies an absolute knowledge about the time at which the photons have been emitted, which in turn implies an absolute uncertainty on their energy. Thus, keeping some information about the frequency of the emitted photons affects the correlations between them. This means that a two-level system can be turned into a versatile source of quantum light, providing light with a large breadth of correlation types well beyond simply antibunching. Furthermore, when the two-level system is driven coherently in the so-called Mollow regime (in which the two-level system becomes dressed by the laser and the emission line is split into three), the correlations blossom: one can find every type of statistics—from antibunching to super-bunching—provided that one measures the photons emitted at the adequate frequency window of the triplet. In fact, the process of filtering the emission at the frequencies corresponding to N-photon transitions is the idea behind the Bundler, a source of light whose emission is always in bundles of exactly N photons. The versatility of the correlations decking the emitted light motivates the topic of this Dissertation, in which I focus on the theoretical study of the behaviour that arises when physical systems are driven with quantum light, i.e., with light that cannot be described through the classical theory of electromagnetism. As the canon of excitation used in the literature is restricted to classical sources, namely lasers and thermal reservoirs, our description starts with the most fundamental objects that can be considered as the optical targets: a harmonic oscillator (which represents the field for non-interacting bosonic particles) and a two-level system (which in turn represents the field for fermionic particles). We describe which regions of the Harmonic oscillator’s Hilbert space can be accessed by driving the harmonic oscillator with the light emitted by a two-level system, i.e., which quantum steady states can be realized. Analogously, we find that the quality of the single-photon emission from a two-level system can be enhanced when it is driven by quantum light. Once the advantages of using quantum, rather than classical, sources of light are demonstrated with the fundamental optical targets, we turn to the quantum excitation of more involved systems, such as the strong coupling between a harmonic oscillator and either a two-level system—whose description is made through the Jaynes-Cummings model—or a nonlinear harmonic oscillator—which can be realized in systems of, e.g., exciton-polaritons. Here we find that the statistical versatility of the light emitted by the Mollow triplet allows to perform Quantum Spectroscopy on these systems, thus gaining knowledge of its internal structure and dynamics, and in particular to probe their interactions with the least possible amount of particles: two. In the process of exciting with quantum light, we are called to further examine the source itself. In fact, there is even the need to revisit the concept of a single-photon source, for which we propose more robust criterion than g(2). We also turn to toy-models of the Bundler so as to use it effectively as an optical source. We can then xix study the advantages that one gets and shortcomings that one faces when using this source of light to drive all the systems considered on excitation with the emission of a two-level system. Finally, we go from the continuous to the pulsed regime of excitation, which is of higher interest for applications and comes with its own set of fundamental questions

2023 Astrophotonics Roadmap: pathways to realizing multi-functional integrated astrophotonic instruments

This is the final version. Available on open access from IOP Publishing via the DOI in this recordData availability statement: The data that support the findings of this study are available upon reasonable request from the authors.Photonic technologies offer numerous functionalities that can be used to realize astrophotonic instruments. The most spectacular example to date is the ESO Gravity instrument at the Very Large Telescope in Chile that combines the light-gathering power of four 8 m telescopes through a complex photonic interferometer. Fully integrated astrophotonic devices stand to offer critical advantages for instrument development, including extreme miniaturization when operating at the diffraction-limit, as well as integration, superior thermal and mechanical stabilization owing to the small footprint, and high replicability offering significant cost savings. Numerous astrophotonic technologies have been developed to address shortcomings of conventional instruments to date, including for example the development of photonic lanterns to convert from multimode inputs to single mode outputs, complex aperiodic fiber Bragg gratings to filter OH emission from the atmosphere, complex beam combiners to enable long baseline interferometry with for example, ESO Gravity, and laser frequency combs for high precision spectral calibration of spectrometers. Despite these successes, the facility implementation of photonic solutions in astronomical instrumentation is currently limited because of (1) low throughputs from coupling to fibers, coupling fibers to chips, propagation and bend losses, device losses, etc, (2) difficulties with scaling to large channel count devices needed for large bandwidths and high resolutions, and (3) efficient integration of photonics with detectors, to name a few. In this roadmap, we identify 24 key areas that need further development. We outline the challenges and advances needed across those areas covering design tools, simulation capabilities, fabrication processes, the need for entirely new components, integration and hybridization and the characterization of devices. To realize these advances the astrophotonics community will have to work cooperatively with industrial partners who have more advanced manufacturing capabilities. With the advances described herein, multi-functional integrated instruments will be realized leading to novel observing capabilities for both ground and space based platforms, enabling new scientific studies and discoveries.National Science Foundation (NSF)NAS

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described