Topological quantization by controlled paths: application to Cooper pairs pumps

Abstract

When physical systems are tunable by three classical parameters, level degeneracies may occur at isolated points in parameter space. A topological singularity in the phase of the degenerate eigenvectors exists at these points. When a path encloses such point, the accumulated geometrical phase is sensitive to its presence. Furthermore, surfaces in parameter space enclosing such point can be used to characterize the eigenvector singularities through their Chern indices, which are integers. They can be used to quantize a physical quantity of interest. This quantity changes continuously during an adiabatic evolution along a path in parameter space. Quantization requires to turn this path into a surface with a well defined Chern index. We analyze the conditions necessary to a {\em Topological Quantization by Controlled Paths}. It is applied to Cooper pair pumps. For more general problems, a set of four criteria are proposed to check if topological quantization is possible.

16 PRB pages

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• Transconductance quantization in a topological Josephson tunnel junction circuit
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• Fast and accurate Cooper pair pump
• Cooper-pair transistor as a minimal topological quantum circuit
• Non-Abelian geometric phases in ground state Josephson devices
• Ground-state geometric quantum computing in superconducting systems
• The Geometry of (non) abelian adiabatic pumping
• Merging diabolical points of a superconducting circuit
• Cooper pair current in the presence of flux noise
• Spectral Signatures of Non-Trivial Topology in a Superconducting Circuit
• Fractional transconductance via non-adiabatic topological Cooper pair pumping
• Topological discretization of bosonic strings
• Adiabatic Cooper-Pair Pumping in a Linear Array of Cooper Pair Boxes