Photon-mediated qubit interactions in 1D discrete and continous models

TL;DR

This paper investigates photon-mediated interactions between two qubits in a 1D waveguide, providing analytical and numerical insights into their effective interactions, spontaneous emission, and spectral properties, highlighting the role of Lamb shifts.

Contribution

It introduces new analytical and numerical methods to analyze qubit interactions in 1D waveguides, emphasizing the impact of Lamb shifts and spectral features.

Findings

Existence of collective Lamb-shifts affecting qubit interactions

Dependence of interactions on qubit separation

Single photon spectroscopy probes renormalized resonances

Abstract

In this work we study numerically and analytically the interaction of two qubits in a one-dimensional waveguide, as mediated by the photons that propagate through the guide. We develop strategies to assert the Markovianity of the problem, the effective qubit-qubit interactions and their individual and collective spontaneous emission. We prove the existence of collective Lamb-shifts that affect the qubit-qubit interactions and the dependency of coherent and incoherent interactions on the qubit separation. We also develop the scattering theory associated to these models and prove single photon spectroscopy does probes the renormalized resonances of the single- and multi-qubit models, in sharp contrast with earlier toy models where individual and collective Lamb shifts cancel.