Instabilities of interacting matter waves in optical lattices with Floquet driving

We experimentally investigate the stability of a quantum gas with repulsive interactions in an optical one-dimensional lattice subjected to periodic driving. Excitations of the gas in the lowest lattice band are analyzed across the complete stability diagram, from slow to fast driving frequencies and from weak to strong driving strengths. To interpret our results, we expand the established analysis based on parametric instabilities to include modulational instabilities. Extending the concept of modulational instabilities from static to periodically driven systems provides a convenient mapping of the stability in a static system to the cases of slow and fast driving. At intermediate driving frequencies, we observe an interesting competition between modulational and parametric instabilities. We experimentally confirm the existence of both types of instabilities in driven systems and probe their properties. Our results allow us to predict stable and unstable parameter regions for the minimization of heating in future applications of Floquet driving.