Scattering Properties of few Waveguide Photons by a Set of Discrete Quantum Systems

The interaction of photons confined in a box with few-level quantum systems has been found to lead to the rich physics of Cavity Quantum Electrodynamics. It is expected that the interaction between discrete quantum systems (hereafter called qubits for simplicity) and strongly confined photons propagating in one-dimension (waveguides) will also lead to remarkable effects, as well as serving a platforms for either inducing qubit-mediated photon-photon interactions of photon-mediated qubit-qubit interactions. Different types of waveguides are being considered: dielectric, photonic crystal, superconducting and metallic (the interest in this case being the potentially strong dipole-photon interaction arising from the confinement of the plasmon field). However, in general the theoretical study of these systems is notoriously difficult because scattering is a many-body problem.

In this paper we present a general theoretical framework for the study of the scattering of N photons, traveling in one dimensional waveguides, due to M qubits.

We will consider both strong and ultrastrong qubit-waveguide photon coupling regimes.

The quantum time evolution is solved via the technique of Matrix Product States, which has been widely used for the computation of low lying energy states in one-dimensional systems of interacting quantum particles but, the the best of our knowledge, has not been used to study scattering properties.

We will pay special attention to the characterization of non-linear effects in different observables (transmission, correlation functions, etc.) as a function of N, M, qubit inter distances and light-matter coupling.

Finally, we will show that the standard result in the case of scattering of one-photon by one-qubit (namely, that scattering is dominated by a reflection resonance appearing when the photon energy coincides with that of excitation of the qubit) is essentially modified for very large photon-qubit interactions. In this case, new processes appear as: Fano resonances, strong renormalization of the reflection resonance and Raman processes reaching unit probability.

lmm@unizar.es