We use high-precision spectroscopy and detailed theoretical modelling to
determine the form of the coupling between a superconducting phase qubit and a
two-level defect. Fitting the experimental data with our theoretical model
allows us to determine all relevant system parameters. A strong qubit-defect
coupling is observed, with a nearly vanishing longitudinal component. Using
these estimates, we quantitatively compare several existing theoretical models
for the microscopic origin of two-level defects.Comment: 3 pages, 2 figures. Supplementary material, lclimits_supp.pd
