Understanding the behavior of superconducting Coulomb-blockade electrometers

We report measurements and quantum mechanical simulations of the behavior of superconducting two-junction Coulomb-blockade electrometers biased near the superconducting gap. Our quantum model allows coherent superpositions of states with different number of charges on the island. It predicts maximum current modulation /spl delta/I for devices with tunneling resistance R/sub /spl Sigma///spl ap/64/spl pi//spl Delta//spl planck//sup 2/C/sub /spl Sigma///sup 2//(e/sup 6//spl tau/), where /spl tau/ is the time for which the system maintains quantum coherence, C/sub /spl Sigma// is the total island capacitance and /spl Delta/ is the superconducting energy gap. For comparison, we built Al-AlO/sub x/-Al electrometers with R/sub /spl Sigma// from 61 k/spl Omega/ to 1.7 M/spl Omega/ and C/sub /spl Sigma// ranging from 0.9 fF to 8 fF. We find good agreement for /spl tau//spl ap/0.35 nsec.