# Uri Vool

Coherent quantum effects are the hallmark of atomic systems. The field of circuit quantum electrodynamics (cQED) also allows for the control of coherent quantum systems. However, these quantum states do no correspond to atomic degrees of freedom, but to the quantized behavior of the electromagnetic field in a marcoscopic superconducting circuit. These "artificial atoms" simulate many of the effects in atomic systems, with the added benefits of tunability and fast control and measurement. This thesis explores the different artificial atoms and quantum operations accessible to us using superconducting circuits, and the techniques we can use to create more interesting and complex atoms. One experiment focuses on selection rules in superconducting circuits. Using non-linear coupling, we are able to break the selection rules of a fluxonium artificial atom and drive forbidden transitions. We use this technique to construct a $\Lambda$ system from the fluxonium coupled to a resonator at the fluxonium sweet spot. Another experiment focuses on the new artificial atoms and operations accesible by adding continuous external drives to the circuit. By taking the Jaynes-Cummings (JC) Hamiltonian of a qubit coupled to a cavity and adding two continuous tones, we are able to simulate an effective JC Hamiltonian in the transverse ($\bm{\sigma_x}$) basis. The energies and interaction terms are completely governed by the drives, and the system can be tuned to any interaction regime in situ. This scheme also allows us to cool the qubit to the eigenstates of the transverse basis, and perform a continuous quantum non-demolition (QND) measurement of the transverse component of a qubit.