Spectroscopy of a driven solid-state qubit coupled to a structured environment

TL;DR

This paper investigates the long-term behavior of a driven solid-state qubit interacting with a structured environment, using exact mappings and analytical techniques to understand resonance phenomena across different damping and temperature regimes.

Contribution

It introduces an exact mapping to analyze the driven qubit-environment system and provides analytical solutions for resonance line shapes in various damping and temperature conditions.

Findings

Multi-photon resonances are identified and analytically characterized.

Resonance line shapes are accurately described in different damping regimes.

The resonance width scales with Bessel functions in the weak damping limit.

Abstract

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the $n$-photon resonance scales with the $n$-th Bessel function of the driving strength in the weak-damping regime.