Current-Phase Relation and Josephson Inductance of Superconducting Cooper Pair Transistor

We have investigated the Josephson inductance $L_J$ of a Superconducting Cooper Pair Transistor (SCPT). We traced the inductance using microwave reflection measurements on a tuned resonance circuit in which a SCPT was mounted in parallel to a $\sim 200$ pH strip line inductance. When the inverse of the Josephson inductance, determined on the charge-phase bias plane for a SCPT with a Josephson to Coulomb energy ratio of $E_J\mathrm{/}{E}_C=1.75$, is integrated over the phase, we obtain a current-phase relation, which is strongly non-sinusoidal near the charge degeneracy point.