Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor

TL;DR

This paper explores how the quantum geometric tensor influences non-adiabatic quantum evolution, revealing how its components affect phase acquisition and trajectories, with practical measurement methods demonstrated in microcavity experiments.

Contribution

It establishes the role of the quantum geometric tensor in non-adiabatic regimes and provides a method to measure its components via light polarization in microcavities.

Findings

Quantum geometric tensor components affect quantum phase and trajectories.

Non-adiabatic corrections can be determined beyond Landau-Zener approximation.

QGT components can be directly measured through polarization in microcavity experiments.

Abstract

We study the role of the quantum geometric tensor (QGT) in the evolution of quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wavepacket in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the non-adiabaticity is determined by the quantum metric (the real part of the tensor) and allows to determine corrections in the regimes where Landau-Zener approach is inapplicable. The particular case of a planar microcavity in the strong coupling regime allows to extract the QGT components by direct light polarization measurements and to check their effects on the quantum evolution.