  We have investigated the decoherence of quantum states in two Al/AlOx/Al
Cooper-pair boxes coupled to lumped element superconducting LC resonators. At
25 mK, the first qubit had an energy relaxation time T1 that varied from 30 us
to 200 us between 4 and 8 GHz and displayed an inverse correlation between T1
and the coupling to the microwave drive line. The Ramsey fringe decay times T2*
were in the 200-500 ns range while the spin echo envelope decay times Techo
varied from 2.4-3.3 us, consistent with 1/f charge noise with a high frequency
cutoff of 0.2 MHz. A second Cooper-pair box qubit with similar parameters
showed T1=4-30 us between 4-7.3 GHz, and that the T1 and the coupling were
again inversely correlated. Although the lifetime of the second device was
shorter than that of the first device, the dependence on coupling in both
devices suggests that further reduction in coupling should lead to improved
qubit performance.
