Mesoscopic Physics

The European Physical Journal B - Condensed Matter and Complex Systems

, Volume 45, Issue 3, pp 405-417

First online:

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

  • M. C. GoordenAffiliated withInstituut-Lorentz, Universiteit Leiden Email author 
  • , M. ThorwartAffiliated withInstitut für Theoretische Physik IV, Heinrich-Heine-Universität Düsseldorf
  • , M. GrifoniAffiliated withInstitut für Theoretische Physik, Universität Regensburg

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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.