Detecting non-Abelian geometric phase in circuit QED

TL;DR

This paper proposes a method to detect the non-Abelian geometric phase in circuit QED systems using three transmon qubits and external magnetic flux control, demonstrating that the noncommutative nature can be experimentally observed.

Contribution

It introduces a novel scheme for detecting non-Abelian geometric phases in circuit QED, utilizing effective tripod interactions and controlled qubit loops.

Findings

Different final states result from different loop orders, confirming noncommutativity.

Numerical simulations show the phase difference is detectable.

The scheme provides a practical way to observe non-Abelian geometric phases.

Abstract

We propose a scheme for detecting noncommutative feature of the non-Abelian geometric phase in circuit QED, which involves three transmon qubits capacitively coupled to an one-dimensional transmission line resonator. By controlling the external magnetic flux of the transmon qubits, we can obtain an effective tripod interaction of our circuit QED setup. The noncommutative feature of the non-Abelian geometric phase is manifested that for an initial state undergo two specific loops in different order will result in different final states. Our numerical calculations show that this difference can be unambiguously detected in the proposed system.