Quantum electrodynamics system for a laser: From cavity QED to waveguide QED

Abstract

The Cavity Quantum Electrodynamics system is the canonical tool for studying the interaction between light and matter, motivated by applications in quantum metrology or quantum computing. In the last years, a new platform is taking importance, the waveguide Quantum Electrodynamics systems. This platform, as well as the cavity case, is used to control the cooperativity of the system, i.e., the rate between the coupling strength of matter (emitters) and the electromagnetic field modes and the dissipation process of the system. Furthermore, this platform presents great versatility in connectivity to other systems, such as fiber optics technologies. Moreover, waveguide QED systems present long-range interaction, promoting collective effects such as superradiance and subradiance, where the guided modes of the electromagnetic field generate correlations between the emitters, enhancing or inhibiting the emission. In this thesis, we present a model of a waveguide QED system laser. This model describes a system of interest that considers the atoms and the modes of the electromagnetic field of the waveguide. This system of interest interacts with a reservoir that considers the pumping mechanism and electromagnetic field modes out of the waveguide. From this model, we derive the Heisenberg-Langevin equation of the system of interest operator. Finally, we present two methodologies to study the spectrum of emission. The first mechanism considers that the electric field is determined by an amplitude defined by the steady-state solution of the bosonic operator s mean-field equation and fluctuations. These fluctuations are ignored. The results of this methodology show that the spectral linewidth is determined by the decay process of the waveguide, and the power of the emission is determined by the pumping parameter and the number of atoms. The second mechanism considers that the field is determined by an amplitude and a phase, and the spectral linewidth is determined by the diffusion process of the phase. The results of this methodology, which consider the effects of fluctuations, show two regimes where the spectrum depends on the decay process of the waveguide and the atoms.