Generation of Ultrahigh Anomalous Hall Conductivities via Optimally Prepared Topological Floquet States

TL;DR

This paper shows how quantum optimal control can design Floquet states with ultrahigh anomalous Hall conductivities, surpassing traditional methods, and enabling new topological transport regimes in ultrafast quantum systems.

Contribution

It introduces a novel optimal control protocol for Floquet states that achieves ultrahigh conductivities and high fidelity, revealing new non-adiabatic topological transport regimes.

Findings

Ultrahigh anomalous Hall conductivities up to 70 times the Chern number.

Optimal protocols reach >99% fidelity at the topological gap closing point.

Achieves these results in as few as ten Floquet cycles, outperforming standard approaches.

Abstract

Ultrafast quantum matter experiments have validated predictions from Floquet theory - notably, the dynamical modification of the electronic band structure and the light-induced anomalous Hall effect, via monotonic modulation of the driving amplitude. Here, we demonstrate how new physics is uncovered by leveraging quantum optimal control techniques to design Floquet amplitude modulation profiles. We discover a fundamentally different regime of topological transport, whereby the optimal oscillatory preparation protocol functions as a non-adiabatic topological pump: as a result, ultrahigh time-averaged anomalous Hall conductivities emerge, that reach up to around seventy times the values one would expect from the Chern number of the targeted Floquet state. The optimal protocols achieve >99% fidelity at the topological energy gap closing point - a twenty-fold improvement over standard monotonic approaches in as little as ten Floquet cycles - while unexpectedly generating the predicted ultrahigh conductivities. Our findings demonstrate that optimally prepared non-equilibrium quantum states can access transport regimes not achievable in the corresponding equilibrium system or even by applying conventional Floquet approaches, opening new avenues for ultrafast quantum technologies and topological device applications.