Cooper Pair Box Qubit in the Ultrastrong Coupling Regime

We propose a new superconducting qubit design, where a small Josephson junction is inserted in the central conductor of a coplanar waveguide resonator. In this distributed element design, the resonator provides a negative reactance for the junction, which modifies the charging energy $E_C$ of the junction and places the qubit far in the ``Transmon regime'', $E_J \gg E_C$, where $E_J$ is the Josephson energy of the junction. We will discuss design details and show preliminary fabrication and measurement results.