Dynamics of a Qubit in a High-Impedance Transmission Line from a Bath Perspective

TL;DR

This paper explores the quantum dynamics of a qubit coupled to a high-impedance transmission line, comparing approximate and exact methods to understand photon scattering and emission, with implications for waveguide QED experiments.

Contribution

It introduces a multimode coherent state approach for light-matter interaction in high-impedance environments and benchmarks it against numerically exact NRG calculations.

Findings

The coherent state approach has limitations in sudden quenches due to spurious correlations.

NRG provides accurate scattering and inelastic loss data in the ultra-strong coupling regime.

Analytical formulas predict transport coefficients and explain inelastic losses near resonances.

Abstract

We investigate quantum dynamics of a generic model of light-matter interaction in the context of high impedance waveguides, focusing on the behavior of the emitted photonic states, in the framework of the spin-boson model Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wavefunction; formally, this approach combines ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we present numerically exact results for scattering of a weak intensity pulse by using NRG calculations. NRG provides a benchmark for any linear response property throughout the ultra-strong coupling regime. We find that in a sudden quantum quench, the coherent state approach produces physical artifacts, such as improper relaxation to the steady state. These previously unnoticed problems are related to the simplified form of the ansatz that generates spurious correlations within the bath. In the scattering problem, NRG is used to find the transmission and reflection of a single photon, as well as the inelastic scattering of that single photon. Simple analytical formulas are established and tested against the NRG data that predict quantitatively the transport coefficients for up to moderate environmental impedance. These formulas resolve pending issues regarding the presence of inelastic losses in the spin-boson model near absorption resonances, and could be used for comparison to experiments in Josephson waveguide QED. Finally, the scattering results using the coherent state wavefunction approach are compared favorably to the NRG results for very weak incident intensity. We end our study by presenting results at higher power where the response of the system is nonlinear.