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

Quantum impurity regime of circuit quantum electrodynamics

In this thesis we describe a novel regime of cavity quantum electrodynamics, where a single atom is coupled to a multi-mode Fabry-Perot cavity with a strength much larger than its free spectral range. In this regime, the atom acting as a quantum impurity mediates interactions between many-body states of radiation in the multi-mode cavity. This novel regime of cavity QED is experimentally realized by coupling superconducting artificial atoms to a high impedance 1-D superconducting transmission line cavity. We study the problem of single photon decay in these strongly non-linear cavities with discrete energy levels. By engineering the properties of the artificial atoms, we alter interaction and connectivity between many-body states of radiation, and we observe two distinct effects. For the case of a multi-mode Fabry-Perot coupled to a fluxonium artificial atom, the interactions mediated by the atom attempts to down convert a single photon into many low frequency photons but fails because of limited connectivity in the many-body Fock space. This phenomenon of many-body localization of radiation gives rise to striking spectral features where a single standing wave resonance of the cavity is replaced by a fine structure of satellite peaks. On the other hand, for the case of a transmon coupled galvanically to the cavity, the interaction splits a single photon at high energy into a shower of odd number of lower energy photons. In this case the single standing wave resonance of the cavity acquires a shorter lifetime which can be calculated using Fermi's golden rule and matches our theoretical model without any adjustable parameters