Eur. Phys. J. B 45, 405-417 (2005)
https://doi.org/10.1140/epjb/e2005-00192-5

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

¹ Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
² Institut für Theoretische Physik IV, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
³ Institut für Theoretische Physik, Universität Regensburg, 93035 Regensburg, Germany

Corresponding author: ^a goorden@lorentz.leidenuniv.nl

Received: 6 December 2004
Published online: 6 July 2005

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 nth Bessel function of the driving strength in the weak-damping regime.