Dissipation in the ultra-strong coupling regime

It has recently been shown that the ultra-strong coupling regime, in which the rotating-wave approximation breaks down, can be obtained using a flux qubit coupled to a transmission line [1]. This regime has been observed experimentally in [2, 3]. We will show the usual quantum optics master equation fails in this context and give a more accurate one. We will also explain how non-trivial properties of the ground state could be experimentally studied.\\[3pt] [1] J. Bourassa et al, Phys. Rev. A 80, 32109 (2009)\\[0pt] [2] T. Niemczyk et al, Nature Physics 6, 772-776 (2010)\\[0pt] [3] P. Forn-D\'iaz et al., arXiv:1005.1559v1 (2010)\\[0pt]