Phonon excitations of Floquet-driven superfluids in a tilted optical lattice

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 micromotion of the superfluids to analyze the growth of phonon modes from slow- to fast-driving frequencies. The model describes phonon excitations in both resonantly and nonresonantly driven systems, with or without a tilted potential. 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.