Topological frequency conversion in strongly driven quantum systems

TL;DR

This paper explores how strongly driven quantum systems can exhibit topologically nontrivial band structures in their Floquet space, leading to quantized energy pumping analogous to topological insulators.

Contribution

It introduces a framework for understanding topological phenomena in multi-frequency driven quantum systems using Floquet lattice representation.

Findings

Demonstrates quantized energy pumping proportional to the Chern number.

Establishes a link between Floquet topology and observable energy transfer.

Provides a model for topological effects in driven two-level quantum systems.

Abstract

When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of {\em irrationally}-related drive frequencies, and the evolution occurs in response to a built-in effective "electric" field, whose components are proportional to the corresponding drive frequencies. The mapping allows to engineer and study temporal analogs of many real-space phenomena. Here we focus on the specific example of a two-level system under two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence of such construction is quantized pumping of energy between the sources with frequencies $\omega_1$ and $\omega_2$. When the system is initialized into a Floquet band with the Chern number $C$, the pumping occurs at the rate $P_{12} = -P_{21}= (C/2\pi)\hbar \omega_1\omega_2$, an exact counterpart of the transverse current in a conventional topological insulator.