Topological frequency conversion in strongly driven 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 $P_{12}=-P_{21}=(C/2\pi )\hslash {\omega }_1{\omega }_2$, an exact counterpart of the transverse current in a conventional topological insulator.

17 pages

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