Tunable current-phase relation in double-dot Josephson junctions

The current-phase relation $I(\varphi)$ for a Josephson junction contains information about the microscopic nature of the Cooper pair transfer. In particular, junctions more complicated than the single tunnel junction exhibit characteristic non-sinusoidal forms. Here, we investigate the Josephson effect in a superconducting double dot device, similar to the devices studied experimentally by Y.\ A.\ Pashkin et al.\ [1] and E.\ Bibow et al.\ [2]. In the vicinity of a charge degeneracy line, the system reduces to a two-level system equivalent to a charge qubit. In this regime, we find that the interplay between sequential tunneling and cotunneling of Cooper pairs leads to a strongly non-sinusoidal current- phase relation, tunable via gate electrodes. We propose the measurement of $I(\varphi)$ in a SQUID configuration, analyze the implications of flux noise, and compare our results to different types of Josephson junctions such as single-dot systems and microbridges. [1] Y.\ A.\ Pashkin et al., Nature (London) \textbf{421} (2003), 823 [2] E.\ Bibow, P.\ Lafarge, L.\ L\'{e}vy, Phys.\ Rev.\ Lett.\ \textbf{88} (2002), 017003