High frequency coupling coefficient between the coplanar resonator and radio frequency SQUID

The coupling coefficient (k/sup 2/) between the superconducting coplanar resonator and the flip chip coupled washer radio frequency SQUID was calculated using computer simulation. The coplanar resonator is formed by two coplanar lines surrounding a flux concentrator with each line having a slit. For a 3 mm/spl times/3 mm washer SQUID with a 100 /spl mu/m/spl times/100 /spl mu/m loop coupled to a coplanar resonator with the slits on opposite sides, we estimated k/sup 2/=7.1/spl times/10/sup -3/. However, if the same SQUID is coupled to a coplanar resonator with parallel slits and with a short circuit at the 90/spl deg/ position with respect to the opening slit, k/sup 2/ of only 0.5/spl times/10/sup -3/ is obtained, which indicates that the k/sup 2/ is strongly dependent on the resonator layout. The simulation also shows that k/sup 2/ is dependent on the SQUID washer size and the separation distance between the washer SQUID and the coplanar resonator.