Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer

Abstract

Demonstration of Majorana non-Abelian properties is a major challenge in the field of topological superconductivity. In this work, we propose a minimal device and protocol for testing non-Abelian properties using charge-transfer operations between a quantum dot and two Majorana bound states combined with reading the parity state using a second dot. We use an adiabatic perturbation theory to find fast adiabatic paths to perform operations and to account for nonadiabatic errors. We find the ideal parameter sweep and a region in parameter space which reduces the charge-transfer operation time 1-2 orders of magnitude with respect to constant velocity driving. Using realistic parameters, we estimate that the lower bound for the time scale can be reduced to $\sim 10$ ns. Deviations from the ideal parameters lead to the accumulation of an undesired dynamical phase, affecting the outcome of the proposed protocol. We furthermore suggest to reduce the influence from the dynamical phase using a flux echo. The echo protocol is based on the $4\pi$-periodicity of the topological state, absent for trivial bound states.

18 pages, 8 figures

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• Semiconductor-ferromagnet-superconductor planar heterostructures for 1D topological superconductivity
• Fusion rules in a Majorana single-charge transistor
• Geometric energy transport and refrigeration with driven quantum dots
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Dynamics of parafermionic states in transport measurements
• Unified model for non-Abelian braiding of Majorana and Dirac fermion zero modes