Bloch oscillations of Fibonacci anyons

Abstract

Non-Abelian anyons, which correspond to collective excitations possessing multiple fusion channels and noncommuting braiding statistics, serve as the fundamental constituents for topological quantum computation. Here, we reveal the exotic Bloch oscillations (BOs) induced by non-Abelian fusion of Fibonacci anyons. It is shown that the interplay between fusion-dependent internal energy levels and external forces can induce BOs and Bloch-Zener oscillations (BZOs) of coupled fusion degrees with varying periods. In this case, the golden ratio of the fusion matrix can be determined by the period of BOs or BZOs in conjunction with external forces, giving rise to an effective way to unravel non-Abelian fusion. Furthermore, we experimentally simulate nonAbelian fusion BOs by mapping Schrodinger equation of two Fibonacci anyons onto dynamical equation of electric circuits. Through the measurement of impedance spectra and voltage evolution, both fusion-dependent BZOs and BOs are simulated. Our findings establish a connection between BOs and non-Abelian fusion, providing a versatile platform for simulating numerous intriguing phenomena associated with non-Abelian physics.