  We study the time and space resolved dynamics of a qubit with an Ohmic
coupling to propagating 1D photons, from weak coupling to the ultrastrong
coupling regime. A nonperturbative study based on Matrix Product States (MPS)
shows the following results: (i) The ground state of the combined systems
contains excitations of both the qubit and the surrounding bosonic field. (ii)
An initially excited qubit equilibrates through spontaneous emission to a
state, which under certain conditions, is locally close to that ground state,
both in the qubit and the field. (iii) The resonances of the combined
qubit-photon system match those of the spontaneous emission process and also
the predictions of the adiabatic renormalization [A. J. Leggett et al., Rev.
Mod. Phys. 59, 1, (1987)]. Finally, a non-perturbative ab-initio calculations
show that this physics can be studied using a flux qubit galvanically coupled
to a superconducting transmission line.
