Nonadiabatic anomalous hall effect for exciton-polaritons

Full text: We derive non-adiabatic corrections to the semiclassical equations of motion of an accelerated wavepacket in a two-band system. We underline the role of the quantum geometric tensor (QGT) and 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 finite-duration experiment. While the adiabatic anomalous Hall effect is determined by the Berry curvature (the imaginary part of the tensor), the non-adiabaticity is determined by the quantum metric gij (the real part of the tensor) and allows us to determine corrections in the regimes where the Landau-Zener approach is inapplicable. The particular case of a planar microcavity in the strong coupling regime, in presence of a non-zero Zeeman field and TE-TM splitting, allows to extract the QGT components by direct light polarization measurements and to check their effects on the quantum evolution of a propagating polariton wave packet through the polariton anomalous Hall effect. Experimental measurement of all the QGT components have been reported for the first time in a high-quality GaAs planar cavity recently. This technique can be extended to measure Bloch band geometries in artificial photonic lattices. (author)