Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving

We derive a topological classification of the steady states $d$-dimensional lattice models driven by $D$ incommensurate tones. Mapping to unifying $(d+D)$-dimensional localized model in frequency space reveals anomalous phases (ALTPs) with no static analog. While formal is determined $d+D$, observable signatures each ALTP depend on spatial dimension $d$. For $d$, $d+D=3$, we identify quantized circulating current, and corresponding edge states. The for wire ($d=1$) function as quantized, nonadiabatic energy pump between drives. design concrete quasiperiodically qubits wires that achieve ALTPs several classes. Our results provide route experimentally access higher dimensional low-dimensional systems.