Topological frequency conversion in a driven dissipative quantum cavity

Recent work [Martin et al., Phys. Rev. X 7, 041008 (2017)] shows that a spin coupled to two externally supplied circularly polarized electromagnetic modes can effectuate a topological, quantized transfer of photons from one mode to the other. Here, we study the effect in the case when only one of the modes is externally provided, while the other is a dynamical quantum mechanical cavity mode. Focusing on the signatures and stability under experimentally accessible conditions, we show that the effect persists down to the few-photon quantum limit and that it can be used to generate highly entangled cat states of cavity and spin. By tuning the strength of the external drive to a sweet spot, the quantized pumping can arise starting from an empty (zero-photon) cavity state. We also find that inclusion of external noise and dissipation does not suppress but rather stabilizes the conversion effect, even after multiple cavity modes are taken into account.