Stability of superfluids in tilted optical lattices with periodic driving

Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their use for probing interacting many-body states. Here, we experimentally investigate phonon modes and interaction-driven instabilities of superfluids in the lowest band of a shaken optical lattice. We identify stable and unstable parameter regions and provide a general resonance condition. In contrast to the high-frequency approximation of a Floquet description, we use the superfluids' micromotion to analyze the growth of phonon modes from slow to fast driving frequencies. Our observations enable the prediction of stable parameter regimes for quantum-simulation experiments aimed at studying driven systems with strong interactions over extended time scales.