Few Photon Photonics in One-Dimensional systems

Luis Martín-Moreno

Instuto de Ciencia de Materiales de Aragón

Light-matter interaction is one of the most fascinating topics in physics. Its enhancement using few-level-systems (FLS) in cavities has lead to the rich field of Cavity Quantum Electrodynamics. More recently, it has been realized that enhanced light-matter interaction can be realized in quasi-one-dimensional waveguides, such as dielectric waveguides, superconducting strips, photonic crystal waveguides, plasmonic waveguides, etc. Different types of waveguides may work at different frequency ranges and different physical conditions (like temperature), but they all profit from the confinement of the field and the reduced dimensionality in light propagation.

Several results are known in these one-dimensional quantum-electrodynamics systems, but the large majority of them have been obtained considering one incoming photon, and within the rotating-wave-approximation, valid for small couplings between the photon field and the FLS, which conserves the total number of excitations (be it a photon or an excitation of the FLS). New effects, and perhaps strong photon-photon interaction mediated by the FLS, are expected when a few photons are launched into the waveguide. However, the theoretical analysis is this many-body situation is notoriously difficult and has only been performed for a few cases concerning two and three photons treated with simplified hamiltonians (as linear photonic dispersion relations in the waveguides and rotating wave approximation).

In this talk we will present a general framework that can address the full many-body situation where any number of photons in a waveguide interact with an arbitrary number of FLS. Our formalism can take into account both the intricacies of non-linear dispersion relations (and thus the existence of band edges) and the full FLS-field hamiltonian (including the counter-rotating terms that do not conserve the number of excitations).

We will present results for the few-level dynamics, transmission and resonant fluorescence as a function of FLS-field coupling, including the so-called ultrastrong coupling regime.