Topological Frequency Conversion in Strongly Driven Quantum Systems

When a physical system is subjected to a strong external multifrequency drive, its dynamics can be conveniently represented in the multidimensional Floquet lattice. The number of Floquet lattice dimensions equals the number of 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 us to engineer and study temporal analogs of many real-space phenomena. Here, we focus on the specific example of a two-level system under a two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence of such a construction is the quantized pumping of energy between the sources with frequencies ω1 and ω2 . When the system is initialized into a Floquet band with the Chern number C , the pumping occurs at a rate P12=−P21=(C/2π)ℏω1ω2 , an exact counterpart of the transverse current in a conventional topological insulator.