Observation of Geometric Phases for Three-Level Systems using NMR Interferometry

TL;DR

This paper reports the first experimental observation of Abelian geometric phases in a three-level quantum system using NMR interferometry, highlighting a novel geometric approach based on $SU(3)/U(2)$.

Contribution

It introduces a new experimental method to measure geometric phases in three-level systems with a unique geometric framework.

Findings

First measurement of Abelian geometric phase in a three-level system

Utilizes NMR interferometry for geometric phase detection

Explores geometry of $SU(3)/U(2)$ in quantum systems

Abstract

Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the first experiment for producing and measuring an Abelian geometric phase shift in a three-level system by using NMR interferometry. In contrast to existing experiments, based on the geometry of $S^2$, our experiment concerns the geometric phase with the geometry of $SU(3)/U(2)$. Two interacting qubits have been used to provide such a three-dimensional Hilbert space.