Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily small $T_2/T_1$ decoherence time ratios

Abstract

We present a perturbative treatment of the subohmic spin-boson model which remedies a crucial flaw in previous treatments. The problem is traced back to the incorrect application of a Markov type approximation to specific terms in the temporal evolution of the reduced density matrix. The modified solution is consistent both with numerical simulations and the exact solution obtained when the bath-coupling spin-space direction is parallel to the qubit energy-basis spin. We therefore demonstrate that %in distinction to previous findings the subohmic spin-boson model is capable of %consistently describing arbitrarily small %(less than two) ratios of the $T_2$ and $T_1$ decoherence times, associated to the decay of the off-diagonal and diagonal reduced density-matrix elements, respectively. An analytical formula for $T_2/T_1$ at the absolute zero of temperature is provided in the limit of a subohmic bath with vanishing spectral power law exponent. Small ratios closely mimic the experimental results for solid state (flux) qubits, which are subject predominantly to low-frequency electromagnetic noise, and we suggest a reanalysis of the corresponding experimental data in terms of a $nonanalytic$ decay of off-diagonal coherence.