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 omega(1) and omega(2). When the system is initialized into a Floquet band with the Chern number C, the pumping occurs at a rate P-12 = -P-21 = (C/2 pi) h omega(1)omega(2), an exact counterpart of the transverse current in a conventional topological insulator.