Supplementary information for the article Intermode Dephasing in a Superconducting Stripline Resonator (arXiv:0901.3110). The supplementary information is devoted to three main issues. In section I we describe the fabrication process; in section II w
e present the derivation of the Hamiltonian of the system and provide a more detailed discussion about the properties of the microbridges; in section III the hysteretic response of the resonator and the effect of heating are discussed.
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 .
We utilize a superconducting stripline resonator containing a dc-SQUID as a strong intermodulation amplifier exhibiting a signal gain of 25 dB and a phase modulation of 30 dB. Studying the system response in the time domain near the intermodulation a
mplification threshold reveals a unique noise-induced spikes behavior. We account for this response qualitatively via solving numerically the equations of motion for the integrated system. Furthermore, employing this device as a parametric amplifier yields a gain of 38 dB in the generated side-band signal.
We study thermal instability in NbN superconducting stripline resonators. The system exhibits extreme nonlinearity near a bifurcation, which separates a monostable zone and an astable one. The lifetime of the metastable state, which is locally stable
in the monostable zone, is measure near the bifurcation and the results are compared with a theory. Near bifurcation, where the lifetime becomes relatively short, the system exhibits strong amplification of a weak input modulation signal. We find that the frequency bandwidth of this amplification mechanism is limited by the rate of thermal relaxation. When the frequency of the input modulation signal becomes comparable or larger than this rate the response of the system exhibits sub-harmonics of various orders.
