Experimental signatures of an extended multifractal phase in a kicked Aubry-André-Harper Hamiltonian

The fractal dimension of quantum matter, defined as a scaling exponent, can acquire multiple values in numerous physical contexts. Such multifractality is commonly observed at a critical point rather than as an extended phase. Here, we experimentally demonstrate that kicked Aubry-André-Harper (kAAH) quasicrystals exhibit a multifractal quantum phase across an extended range in parameter space. These experiments use Bose-Einstein condensates of strontium atoms loaded into an optical lattice and kicked with a secondary lattice of an incommensurate wavelength. To eliminate interband heating and preserve the tight-binding character of the Hamiltonian, we engineer the kick waveforms based on a multiband time-domain model, a technique analogous to apodization in optics or RF engineering. This enables access to a phase diagram spanning a parameter space 5 orders of magnitude larger than that accessible with simple kicking schemes. Transport measurements show signatures of the extended multifractal phase and anomalous disorder-driven re-entrant delocalization.