Waveguide QED: Multiple Qubits, Inelastic Scattering, and Non-Markovianity

Abstract

Waveguide quantum electrodynamics (QED) studies multi-level systems (or qubits) strongly interacting with one-dimensional (1D) light fields confined in a waveguide. This rapidly growing research field attracts much attention because it provides a fascinating platform for many-body physics, quantum nonlinear optics, as well as open quantum systems (OQS). On this platform, researchers are able to control single qubit using single photons and vice versa, based on which many potential applications in quantum information processing and quantum computing are proposed. Due to the reduced dimensionality, the coupling between light and matter is greatly enhanced and so is the light interference. This, together with the strong nonlinearity provided by the qubits, results in striking quantum-optical effects at the few-photon level, which have been demonstrated experimentally in the past few years on various systems such as superconducting circuits thanks to the explosive experimental progress.While much has been known with regard to a single qubit in an infinite waveguide, it is less understood how multiple qubits would reshape the properties of 1D light. For instance, there can be effective interaction between a pair of qubits in a waveguide even in the absence of dipole-dipole interaction, which in turn causes a splitting in the power spectra and interesting bunching and anti-bunching effects for the photons. Moreover, from the OQS point of view, the systems (qubits) and its environment (photons) are highly correlated, so it is natural to question and test the validity of Markovian dynamics in a waveguide-QED setup.In this thesis, I consider two or more distant qubits present in a waveguide under weak driving. The role of inelastic scattering and its connection to dark states and photon correlations are emphasized. I report two-photon scattering wavefunction for multiple qubits (N>2) in an infinite or semi-infinite waveguide. The latter has a perfect mirror at the end that reflects all of the incident photons. I find that by tuning the separation between each qubit it is possible to have stronger (anti-)correlations compared to the single-qubit case, and that the correlation can last over hundreds of the lifetime of a single qubit. The inelastic scattering is highly sensitive to the qubit-qubit (or qubit-mirror) separation and the incident frequency due to the narrow widths caused by the dark states. I also investigate the differences in scattering due to the level structure of the qubits, including two-level systems (2LS), three-level systems (3LS), and their mixture. For example, I find that a "2-3-2" setup --- two distant 2LS sandwiching a 3LS --- can either rectify photons or induce correlation among elastically transmitted photons.I further propose a simple waveguide-QED system as a model system for OQS studies owing to its complex yet exactly solvable nature. To this end, a time-dependent scattering is considered, from which a dynamical map describing the system evolution can be obtained. In combination with OQS tools, I present detailed analysis for the non-Markovian properties of the system, and point out that the scattering setup generally gives rise to a different class of dynamical maps that are largely unexplored in conventional OQS studies. The parameters considered throughout this thesis are fully accessible with existing experimental technology, so realistic tests of my work are within reach.