Floquet Supersymmetry

We introduce the notion of time-reflection symmetry in periodically driven (Floquet) quantum systems, and show that it enables a Floquet variant of quantum-mechanical supersymmetry. In particular, we find Floquet analogues of the Witten index that place lower bounds on the degeneracies of states with quasienergies 0 and π. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies 0,π, which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.