Integration of the Berry curvature on a qubit state manifold by coupling to a quantum meter system

TL;DR

This paper proposes a method to measure the Chern number of a qubit state manifold by coupling it to a meter system and integrating the Berry curvature through a quasi-adiabatic process, accounting for measurement disturbance.

Contribution

It introduces a continuous coupling scheme to estimate the Chern number and a protocol to cancel dynamic phase effects, enhancing measurement accuracy in quantum systems.

Findings

The meter's observable change estimates the Chern number.

A correction factor accounts for qubit disturbance.

A three-step protocol cancels dynamic phase effects.

Abstract

We present a scheme that allows integration of the Berry curvature and thus determination of the Chern number of a qubit eigenstate manifold. Our proposal continuously couples the qubit with a meter system while it explores a quasi-adiabatic path in the manifold. The accumulated change of one of the meter observables then provides an estimate of the Chern number. By varying the initial state of the meter, we explore the delicate interplay between the measurement precision and the disturbance of the qubit. A simple argument yields a correction factor that allows estimation of the Chern number, even when the qubit is significantly disturbed during the probing. The Chern number arises from the geometric phase accumulated during the exploration, while we observe the dynamic phase to produce a broadening of the meter wave function. We show that a protocol, relying on three subsequent explorations, allows cancellation of the dynamic phase while the geometric phase is retained.