In this paper we derive the environmental spectral density for flux, phase and charge qubits when each of them is coupled to an environment with a resonance. From the spectral density we obtain the characteristic spontaneous emission (relaxation) lifetimes T1 for each of these qubits, and show that there is a substantial enhancement of T1 beyond the resonant frequency of the environment.
@article{arxiv.0805.2419,
title = {Spectral densities of superconducting qubits with environmental resonances},
author = {Kaushik Mitra and C. J. Lobb and C. A. R. Sá de Melo},
journal= {arXiv preprint arXiv:0805.2419},
year = {2008}
}