Topological anomalous Floquet photon pump*

We propose an experimentally viable protocol to realize non-adiabatic topological photon pumping mediated by a single qubit, which we dub the anomalous Floquet photon pump. For both quantized and non-quantized photons, the system exhibits a non-trivial topological phase across a broad range of parameter space. Transitions out of the topological phase transition result from frequency-space delocalization. Finally, we argue that the protocol can be implemented in existing experiments via driven qubit non-linearities, with topological pumping witnessed in measurements of the cavity Wigner distribution functions.