Non-Abelian Superconducting Pumps

Cooper pair pumping is a coherent process. We derive a general expression for the adiabatic pumped charge in superconducting nanocircuits in the presence of level degeneracy and relate it to non-Abelian holonomies of Wilczek and Zee. We discuss an experimental system where the non-Abelian structure of the adiabatic evolution manifests in the pumped charge.

Figure 1

Non-Abelian superconducting pump. The gate voltages are kept fixed during the cycle, their values are chosen in order to have a doubly degenerate spectrum. The only pumping parameters are the fluxes through the four loops.

Figure 2

By varying the Josephson couplings through the cycles ${\zeta }_L$ (left) and then ${\zeta }_R$ (right) one Cooper pair is transferred through the pump.

Figure 3

Noncommuting cycles in the parameters space. Along ${\zeta }_1$, $J_2$ is set to zero while along ${\zeta }_2$, both $J_L$ and $J_R$ are fixed. The circles indicate the initial points of each cycle.