  We study superconducting stripline resonator (SSR) made of Niobium, which is
integrated with a superconducting interference device (SQUID). The large
nonlinear inductance of the SQUID gives rise to strong Kerr nonlinearity in the
response of the SSR, which in turn results in strong coupling between different
modes of the SSR. We experimentally demonstrate that such intermode coupling
gives rise to dephasing of microwave photons. The dephasing rate depends
periodically on the external magnetic flux applied to the SQUID, where the
largest rate is obtained at half integer values (in units of the flux quantum).
To account for our result we compare our findings with theory and find good
agreement. Supplementary info at arXiv:0901.3133 .
