An experimental proposal to observe non-abelian statistics of Majorana-Shockley fermions in an optical lattice

TL;DR

This paper proposes an experimental method using cold atoms in optical lattices to observe non-abelian statistics of Majorana-Shockley fermions, including creation, braiding, and detection of topological qubits.

Contribution

It introduces a practical scheme for manipulating Majorana-Shockley modes in optical lattices, enabling observation of non-abelian statistics through adiabatic control and local measurements.

Findings

Majorana-Shockley modes obey non-abelian statistics

Braiding operations are robust against noise and imperfections

Detection via local atom number measurement is feasible with current technology

Abstract

We propose an experimental scheme to observe non-abelian statistics with cold atoms in a two dimensional optical lattice. We show that the Majorana-Schockley modes associated with line defects obey non-abelian statistics and can be created, braided, and fused, all through adiabatic shift of the local chemical potentials. The detection of the topological qubit is transformed to local measurement of the atom number on a single lattice site. We demonstrate the robustness of the braiding operation by incorporating noise and experiential imperfections in numerical simulations, and show that the requirement fits well with the current experimental technology.