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We study the role of the quantum geometric tensor (QGT) in the evolution ofquantum systems. We show that all its components play an important role on theextra phase acquired by a spinor and on the trajectory of an acceleratedwavepacket in any realistic finite-duration experiment. While the adiabaticphase 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 thetensor) and allows to determine corrections in the regimes where Landau-Zenerapproach is inapplicable. The particular case of a planar microcavity in thestrong coupling regime allows to extract the QGT components by direct lightpolarization measurements and to check their effects on the quantum evolution.

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