During the last twenty years, ultracold atoms in optical lattices have emerged as powerful quantum simulators for the physics of interacting electrons in solids. They have e.g. been used to study effects of strong correlations (Mott insulators), disorder and topology. In more than one dimension, these studies have mostly been restricted to periodic potentials, such as those in regular crystals.
In condensed matter systems, however, there exist also alternatives to simple periodic crystals. Quasicrystals are a novel form of condensed matter that is non-periodic, but long-range ordered. They have first been observed in the 1980s by Dan Shechtman in diffraction experiments. Quasicrystals give rise to a pattern of sharp Bragg peaks, similar to periodic crystals, but with rotational symmetries that are impossible for periodic structures. Their structure was found to be given by aperiodic tilings with more than one unit cell, such as the celebrated Penrose tiling.
Even though quasicrystals are long-range ordered, many foundational concepts of periodic condensed matter systems such as Blochwaves or Brillouin zones are not applicable. This places them on an interesting middle ground between periodic and disordered systems and highlights their potential for novel many-body physics.
The main objective of this proposal has been to extend the level of control provided by optical lattices to quasiperiodic potentials by realizing an optical quasicrystal.
The project was successful and we were able to realize an eightfold symmetric optical quasicrystal for ultracold atoms and to demonstrate the fractal crystal structure, the mapping to 4D periodic lattices, and to observe the long sought-after superfluid to Bose glass transition.
