Engineering spatially inhomogeneous tunneling in shaken lattices

We present theoretical and experimental evidence of the creation of position-dependent tunneling by Floquet engineering in a 1D bichromatic optical lattice. When the lattice is driven in a way which maps to illumination with circularly polarized light in a higher-dimensional model, tunneling matrix elements acquire sinusoidal spatial dependence. When the bichromatic lattice is quasiperiodic, this inhomogeneous tunneling creates a multifractal phase of matter with self-similar eigenstates, without any fine-tuning of parameters. We experimentally measure transport of a condensate expanding in such a driven lattice, and extract the subdiffusive transport exponents in a parameter region corresponding to the multifractal phase, providing experimental evidence for the creation of spatially inhomogeneous tunneling. In a periodic bichromatic lattice, the locations where the tunneling changes sign can create effective event horizons. Our results lead to a generalizable recipe for the creation of complex tunneling landscapes in optical lattices using simple global periodic modulation.