Floquet Supersymmetry

We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical supersymmetry. In particular, we find Floquet analogs of the Witten index that place lower bounds on the degeneracies of states with quasienergies 0 and π. Moreover, we show that in some cases time-reflection symmetry can also interchange fermions and bosons, leading to fermion-boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies 0 and 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.