Two-Photon Scattering in USC regime

TL;DR

This paper investigates two-photon scattering in the ultrastrong coupling regime of a two-level system coupled to a waveguide, providing analytical predictions using a polaron approach for certain coupling strengths.

Contribution

It introduces a polaron Hamiltonian approximation for the USC regime and derives analytical scattering matrices for single- and two-photon processes.

Findings

Validates the polaron approximation for coupling strengths up to =1

Provides analytical expressions for scattering matrices in the USC regime

Shows the dynamics are well captured by a conserved excitation number approximation

Abstract

In this work we study the scattering of pairs of photons by a two-level system ultrastrongly coupled to a one-dimensional waveguide. We describe this problem using a spin-boson model with an Ohmic environment $J(\omega)=\pi\alpha\omega^1.$ We show that when coupling strength lays is about $\alpha\leq 1,$ the dynamics is well approximated by a polaron Hamiltonian, under the approximation of a conserved number of excitations. In this regime, we develop analytical predictions for the single- and two-photon scattering matrix computed with a Green's function method.