  Environmental influences on the dynamics of a coupled qubit-oscillator system
are studied analytically. We investigate the case of a quasi-degenerate qubit
within the ultra-strong coupling regime for which the qubit frequency is much
smaller than the frequency of the oscillator, and the coupling between the
qubit and the oscillator is large, both of which invalidate the usually
employed rotating wave approximation. In contrast to the standard quantum
optics master equation, we explicitly take the qubit-oscillator coupling into
account while microscopically deriving a dressed state master equation. Using
the derived master equation, we discuss a spectroscopic technique which can be
used to probe the dressed energy level structure of the qubit-oscillator
system.
