Elliptical rotation of a bosonic oscillator in ultrastrong waveguide QED

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