A 10-fold Symmetric Quasicrystal Quantum Simulator
Quasicrystals are aperiodic but still have long-range order; they possess crystallographically forbidden rotational symmetry but not translational symmetry. In 1984, Shechtman performed X-ray diffraction measurements on an aluminum manganese alloy, revealing 10-fold rotational symmetry in the diffraction pattern. This work, initially rejected by many peers, eventually led to the redefinition of what constitutes a crystal. Shechtman was then awarded the 2011 Nobel prize in chemistry.
Electronic band structure and topology, which would typically provide insight into material properties of periodic crystals, are still not well-understood for quasicrystals because standard theoretical methods used to study band structure rely on translational symmetry. Quantum simulation of a quasicrystalline lattice would open a window into quasicrystal band structure and topology that is largely inaccessible to theory.
This talk will detail the design of an ultra-cold lithium experiment with a 10-fold symmetric optical lattice: a quasicrystal quantum simulator. The first experiments of this simulator will involve diffraction of a Bose-Einstein condensate from the quasicrystalline optical lattice potential. This proof-of-concept experiment will pave the way to follow-up experiments with Bose condensates and degenerate Fermi gases in dynamical quasicrystal lattices, such as the mapping of intriguing features in quasicrystalline band structures that have deep connections to the properties of quasicrystalline topological quantum materials.
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