The first experimental result from the Quasicrystal lab, showing the fractal nature of the potential as well as the connection to a 4D crystal, has now been published as an Editor's suggestion in PRL.
Quasicrystal Paper published in PRL
Ultracold atoms in optical lattices are used as versatile quantum simulators to shed light on a large variety of problems in many-body physics. In this experiments, atoms take the roles of electrons in solids, while the crystal structure is imposed externally using laser light.
In this work, which has now been published as an Editor's suggestion in PRL, we have moved beyond traditional periodic lattices and have engineered an optical quasicrystal. Quasicrystals are intriguing states of matter that occupy a fascinating middle ground between periodic crystals and amorphous unordered glasses—they are long-range ordered without being periodic. Quasicrystals are self-similar and their fractal structure can give rise to the most complex quantum states. Mathematically, they can be described as a projection from a in our case four-dimensional periodic parent lattice.
In our experiments, we create an eightfold symmetric optical quasicrystal by interfering eight laser beams in a plane and reveal the peculiarities of the resulting structure by applying short pulses of the optical lattice to a Bose Einstein condensate. We observe fractal diffraction images that are very similar to the original diffraction pictures of electronic quasicrystals, for which Dan Shechtman was recently awarded the Nobel Prize in chemistry. We furthermore study the time-dependence of the diffraction process and find a direct correspondence between our quasicrystal and a four-dimensional hypercube.
These measurements enable future studies of higher-dimensional physics in ultracold-atom systems, with exciting applications in condensed matter and high-energy physics. Moreover, our experimental setup allows studying quasicrystals with strongly interacting atoms. Defining the precise role of interactions in disordered quantum systems is one of the big challenges in many-body physics and we are now in the position to provide much-needed experimental evidence for addressing these open question.