Quantum dynamics of a qubit coupled with structured bath

Abstract

The dynamics of an unbiased spin-boson model with Lorentzian spectral density is investigated theoretically in terms of the perturbation theory based on a unitary transformation. The non-equilibrium correlation function $P(t)$ and susceptibility ${\chi }^{\prime \prime }(\omega )$ are calculated for both the off-resonance case $\Delta \lesssim 0.5\Omega$ and the on-resonance case $\Delta \sim \Omega$. The approach is checked by the Shiba's relation and the sum rule. Besides, the coherent-incoherent transition point ${\alpha }_c$ can be determined, which has not been demonstrated for the structured bath by previous authors up to our knowledge.

25 pages, 11 figures

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