Quantum Anomalous Floquet states in cavity QED materials

Floquet engineering has provided a route to externally control quantum systems by means of classical fields. This is achieved by periodically driving a system with a suitable external field, such that the stroboscopic dynamics can be approximately described by a tunable target Hamiltonian.

Recently, advances in the experimental realization of cavities coupled to quantum systems have provided the possibility to also use quantized fields, developing the field of cavity QED materials. In this context, it has been formally shown that features of Floquet physics can be recovered in the classical limit.

This creates an interesting paradigm because Floquet systems do not conserve energy due to the existence of an external driving field, while cavity QED materials are isolated quantum systems. We explore this relation by looking for the analog of Anomalous Floquet topological phases in cavity QED materials. This is a special case because they are distinctive phases of Floquet systems without a static analog. We find that Quantum Anomalous Floquet phases are strongly correlated topological phases of light and matter that emerge when the two system are resonantly interacting. There, two types of topologically protected states coexists such that the topological invariant of the many-body wave-function vanishes. However, we show that the invariant can be separated in two invariants that are non-vanishing, each describing a different type of edge state.