Cooper-pair pump as a quantized current source

A new charge quantization in a phase-polarized Cooper-pair pump is proposed, based on the topological properties of its Hamiltonian ground state over a three-dimensional parameter space P. The charge is quantized using a set of paths in P covering the surface of a torus, and is a multiple of the integer Chern index c(1) of this surface. This quantization is asymptotic but the pumped charge converges rapidly to the quantized value with the increase in the path frequency. The topological nature of the current makes this Cooper-pair pump implementation an excellent candidate for a metrological current standard.