Exciting with quantum light

Abstract

A 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.