Quasi-Lumped Element Resonator Coupled to a Cooper-Pair Box

We have coupled a ``quasi-lumped element'' microwave resonator ($f_{0}$ = 5.433 GHz), made of superconducting Al on sapphire, to an Al/AlO$_{\mbox{x}}$/Al Cooper-pair box (CPB) qubit. In zero magnetic field, the CPB is far detuned from the resonator and we measure a 50 kHz decrease in $f_{0}$ with the qubit in the ground state and near the degeneracy point of the CPB. By exciting the CPB from the ground state using a second microwave tone and monitoring the transmission through our resonator, we have determined that our CPB has a charging energy $E_{C}/h$ = 12.5 GHz and a maximum $E_{J}/h$ = 9 GHz. By changing the external magnetic field, we can also decrease the effective $E_ {J}$ of the CPB. This decreases the detuning between the CPB and resonator and increases the frequency shift of the resonator. From modeling our data, we extract a coupling strength of $g/2\pi$ = 11 MHz [1,2]. Single and two tone spectroscopy of this system will be presented as well as preliminary measurements of $T_{1}$ and $T_{2}^*$. [1] Alexandre Blais \emph{et al}., Phys. Rev. A \textbf{69}, 062320 (2004). [2] A. Wallraff \emph{et al}., Nature \textbf{431}, 162 (2004).