Non-Abelian geometric phases in ground state Josephson devices

TL;DR

This paper proposes a superconducting circuit that demonstrates non-Abelian geometric phases through adiabatic ground state evolution, enabling experimental observation via charge measurements.

Contribution

It introduces a novel superconducting device that realizes non-Abelian geometric phases in the ground state, differing from previous methods that relied on excited states.

Findings

Non-Abelian phases can be observed through pumped charge measurements.

Transition from non-Abelian to Abelian cycles is experimentally detectable.

The device enables direct measurement of geometric phases using charge sensors.

Abstract

We present a superconducting circuit in which non-Abelian geometric transformations can be realized using an adiabatic parameter cycle. In contrast to previous proposals, we employ quantum evolution in the ground state. We propose an experiment in which the transition from non-Abelian to Abelian cycles can be observed by measuring the pumped charge as a function of the period of the cycle. Alternatively, the non-Abelian phase can be detected using a single-electron transistor working as a charge sensor.