Self and Cross Kerr effects in a Josephson junction chain.

We have performed microwave transmission measurements on propagation modes in Josephson junction chains containing several hundreds of junctions. After some preliminary measurements [1] we have done a more systematic measurement in an improved measurement-set-up. Some of the chains have been embedded into a microwave strip line, while others have been coupled capacitively to it. The latter configuration enables a study of the internal quality factor of the chain while the first one is more suited to study quantitatively the Kerr effects occurring between different modes in the chain. The experimental dispersion curve fits well the theoretical prediction. We measured the Self- and Cross Kerr effects by two-tone spectroscopy measurements. We deduce from our measurements the Self- and Cross Kerr coefficients for the first 8 modes and compare them to theory. [1] T. Weissl, B. Kueng, E. Dumur, A. K. Feofanov, I. Matei, C. Naud, O. Buisson, F. W. J. Hekking, and W. Guichard Phys. Rev. B 92, 104508 (2015)