Lifetime and Coherence of Two-Level Defects in a Josephson Junction

We measure the lifetime ($T_{1}$) and coherence ($T_{2}$) of two-level defect states (TLSs) in the insulating barrier of a Josephson phase qubit and compare to the interaction strength between the two systems. We find for the average decay times a power law dependence on the corresponding interaction strengths, whereas for the average coherence times we find an optimum at intermediate coupling strengths. We explain both the lifetime and the coherence results using the standard TLS model, including dipole radiation by phonons and anti-correlated dependence of the energy parameters on environmental fluctuations.