Two-dimensional optical quasicrystal potentials for ultracold atom experiments

Localization in Two-Dimensional Quasicrystalline Lattices

We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for (6ER,9ER), while it occurs in the interval (12ER,15ER) for octagonal and dodecagonal symmetries.

Construction of photorefractive photonic quasicrystal microstructures by twisted square lattices

A convenient method to fabricate two-dimensional photonic quasicrystal microstructures was experimentally demonstrated by using a rotatable four-wedge prism. Two-dimensional eightfold symmetric quasicrystal microstructures are formed by two groups of twisted square lattices in a photorefractive crystal. The experimental devices of this method are simple and stable without complicated optical adjustment equipment. Optical-induced quasicrystal microstructures are analyzed and verified by magnified imaging and far-field diffraction pattern imaging. The method can be extended to fabricate more complex quasicrystal and moiré lattice microstructures. We numerically demonstrate that this method can be used to fabricate other complex photonic microstructures by using different multi-wedge prisms and adjusting the rotation angle properly.

Phase Transformation of High Velocity Air Fuel (HVAF)-Sprayed Al-Cu-Fe-Si Quasicrystalline Coating

Al-Cu-Fe-Si quasicrystalline coatings were prepared by high velocity air fuel spraying to study their phase transformation during the process. The feedstock powder and coating were phase characterized by scanning electron microscopy, X-ray diffractometry, differential scanning calorimetry, and transmission electron microscopy. Results show that Al3Cu2 phase, a small amount of λ-Al13Fe4 phase, quasicrystalline phase (QC), amorphous phase, and β-Al (Cu, Fe, Si) phase were present in the sprayed Al50Cu20Fe15Si15 powder. For a typical flattened powder particle, the splat periphery was surrounded by a 1 µm thick amorphous phase. The inside area of the splat was composed of the QC covered by the Al3Cu2 and Si-rich β-Al (Cu, Fe, Si) phases. Another kind of Cu- rich β-Al (Cu, Fe, Si) phase can be found close to the amorphous area with a similar composition to the original β-Al (Cu, Fe, Si) phase in the powder. Different phases were observed when the periphery and inside area of the splat were compared. This result was caused by the difference in the heating and cooling rates.

Phasonic Spectroscopy of a Quantum Gas in a Quasicrystalline Lattice

Phasonic degrees of freedom are unique to quasiperiodic structures and play a central role in poorly understood properties of quasicrystals from excitation spectra to wave function statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectroscopy of a quantum gas in a one-dimensional quasicrystalline optical lattice. We observe that strong phasonic driving produces a nonperturbative high-harmonic plateau strikingly different from the effects of standard dipolar driving. Tuning the potential from crystalline to quasicrystalline, we identify spectroscopic signatures of quasiperiodicity and interactions and map the emergence of a multifractal energy spectrum, opening a path to direct imaging of the Hofstadter butterfly.

Topological Phases without Crystalline Counterparts

We construct a two-dimensional higher-order topological phase protected by a quasicrystalline eightfold rotation symmetry. Our tight-binding model describes a superconductor on the Ammann-Beenker tiling hosting localized Majorana zero modes at the corners of an octagonal sample. In order to analyze this model, we introduce Hamiltonians generated by a local rule, and use this concept to identify the bulk topological properties. We find a Z_{2} bulk topological invariant protecting the corner modes. Our work establishes that there exist topological phases protected by symmetries impossible in a crystal.