Elliptical rotation of cavity amplitude in ultrastrong waveguide QED

TL;DR

This paper rigorously analyzes the optical response of a waveguide QED system in the ultrastrong coupling regime, revealing elliptical cavity amplitude motion caused by counter-rotating terms and an asymmetric reflection coefficient.

Contribution

It provides an exact diagonalization approach to study ultrastrong coupling effects, highlighting elliptical cavity motion and its impact on reflection properties.

Findings

Elliptical cavity amplitude motion due to counter-rotating terms.

Large Lamb shift causes notable elliptical motion in ultrastrong regime.

Asymmetric reflection coefficient with respect to resonance frequency.

Abstract

We investigate optical response of a linear waveguide quantum electrodynamics (QED) system, namely, an optical cavity coupled to a waveguide. Our analysis is based on exact diagonalization of the overall Hamiltonian and is therefore rigorous even in the ultrastrong coupling regime of waveguide QED. Owing to the counter-rotating terms in the cavity-waveguide coupling, the motion of cavity amplitude in the phase space is elliptical in general. Such elliptical motion becomes remarkable in the ultrastrong coupling regime due to the large Lamb shift comparable to the bare cavity frequency. We also reveal that such elliptical motion does not propagate into the output field and present an analytic form of the reflection coefficient that is asymmetric with respect to the resonance frequency.