Microwave Photos in High Impedance Transmission line: Dispersion, Disorder and Localization

In this thesis we will describe the theoretical and experimental studies of a TEM on-chip superconducting transmission line with a wave impedance as high as 20 $\mathrm{k}\Omega$, phase and group velocity of waves simultaneously reduced by a factor of 100 in a broad range of frequencies from 0 to about 10 $\mathrm{GHz}$. A conventional microwave coaxial transmission line gets its inductance and capacitance from magnetic and electric fields stored in the space between its inner and outer conductors. This in turn limits its impedance to around 50 $\Omega$ and group velocity of waves very close to the speed of light in vacuum. In this work we are able to increase the impedance by over two orders of magnitude and reduce the group and phase velocity of waves by over two orders of magnitude as well, by constructing a coplanar transmission line out of a pair of long Al/AlOx/Al Josephson tunnel junction chains. A Josephson junction gets its inductance not from the magnetic energy but rather from the much larger kinetic energy of tunneling Cooper pairs, which is unrelated to the electromagnetic properties of vacuum. In this work we present a design of such a transmission line and low-temperature measurement of its dispersion relation. We then study and characterize the disorder present in the circuit parameters of our system and using this, we conclude that for frequencies up to 12 GHz, there is no evidence of Anderson localization of waves, even for chains exceeding 30,000 junctions. Low dissipation and absence of localization make this transmission line ideal for use in various experiments where high impedance can enable strong coupling between light and matter