Observation of 0.2 ms Lifetime in a Cooper-pair Box

We have coupled a quasi-lumped element superconducting microwave resonator with a resonant frequency of 5.44 GHz to an Al/AlO$_{\mbox{x}}$/Al Cooper-pair box (CPB) charge qubit. The resonator is in turn weakly coupled to a transmission line and shows no higher resonant modes up to 20 GHz. By monitoring perturbations of the resonant frequency, we have measured the spectrum and lifetime ($T_{1}$) of the CPB at the charge degeneracy point while the CPB was detuned from the resonator by up to 3.5 GHz. The maximum $T_{1}$ of the CPB was 200 $\mu$s for $f$ = 4 to 4.5 GHz, while $T_{1}$ decreased to 4 $\mu$s around 8 GHz. Our measured $T_{1}$'s imply that the loss tangent in the AlO$_{\mbox{x}}$ junction barrier must be less than about $4\times 10^{-8}$ at 4.5 GHz, about 4 orders of magnitude less than reported in larger area Al/AlO$_{\mbox{x}}$/Al tunnel junctions.