Relaxation of Josephson qubits due to strong coupling to two-level systems

We investigate the energy relaxation (T-1) process of a qubit coupled to a bath of dissipative two-level fluctuators (TLFs). We consider the fluctuators strongly coupled to the qubit both in the limit of spectrally sparse single TLFs as well as in the limit of spectrally dense TLFs. We conclude that the avoided level crossings, usually attributed to very strongly coupled single TLFs, could also be caused by many weakly coupled spectrally dense fluctuators.