Quasicrystals: What do we know? What do we want to know? What can we know?

Steurer, Walter

doi:10.1107/s2053273317016540

Cited by 97 publications

(73 citation statements)

References 77 publications

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“…Their order can be considered to arise from incommensurate projections of higher-dimensional periodic crystals [4,5], or due to a continous tiling of space with discrete unit cells [6]. Over the last few decades, quasicrystals have been studied in condensed matter systems [3,7,8], photonics [9,10], twisted bilayer graphene [11], the Gross-Pitaevskii equation with solitons [12], and as an emergent phase in ultracold dipolar gases [13]. There has also been a significant amount of research into the case of one-dimensional disordered, quasirandom and/or incommensurate systems that are related to quasicrystals [14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Mean-field phases of an ultracold gas in a quasicrystalline potential

2019

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The recent experimental advancement to realise ultracold gases scattering off an eight-fold optical potential [Phys. Rev. Lett. 122, 110404 (2019)] heralds the beginning of a new technique to study the properties of quasicrystalline structures. Quasicrystals possess long-range order but are not periodic, and are still little studied in comparison to their periodic counterparts. Here, we consider an ultracold bosonic gas in an eight-fold symmetric lattice and assume a toy model where the atoms occupy the ground states of the local minima of the potential. The ground state phases of the system are studied, with particular interest in the local nature of the phases. The usual Mott-insulator, density wave, and supersolid phases of the standard and extended Bose-Hubbard model are observed. For non-zero long-range interactions, we find that density wave states can spontaneously break the eight-fold symmetry, and may even possess no rotational symmetry. We find the local variation in the number of nearest neighbours to play a vital role in the phase transitions, local structure, and global symmetries of the ground states. This variation in the number of nearest neighbours is not a unique property of the considered eight-fold lattice, and we expect our results to be generalisable to any quasicrystalline potential where there are only small position dependent variations in the site energy, tunnelling and interactions.

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Section: Introductionmentioning

confidence: 99%

Mean-field phases of an ultracold gas in a quasicrystalline potential

2019

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“…Important manifestations of this non-trivial order on all length scales include the absence of universal power-law scaling near criticality [15] and its application to quantum complexity [16]. Moreover, quasicrystals exhibit fascinating phenomena such as phasonic degrees of freedom [6,17,18]. To date, quasicrystals have been extensively studied in condensed matter and material science [1,3,4,6,17], in photonic structures [9,13,[18][19][20], using laser-cooled atoms in the dissipative regime [21,22], and very recently in twisted bilayer graphene [23].…”

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confidence: 99%

“…standing waves of light, have become a cornerstone in experimental research on quantum manybody physics [25]. They offer an ideal environment for examining quasicrystals since optical potentials are free of defects which greatly complicate measurements on quasicrystalline solids [6]. In addition, we are able to directly impose 'forbidden' rotational symmetries, thereby circumventing the elaborate synthesis of stable single crystals [26].…”

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confidence: 99%

Matter-Wave Diffraction from a Quasicrystalline Optical Lattice

et al. 2019

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Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of non-trivial structure on all scales. Here we report on the first experimental demonstration of an eightfold rotationally symmetric optical lattice, realising a twodimensional quasicrystalline potential for ultracold atoms. Using matter-wave diffraction we observe the self-similarity of this quasicrystalline structure, in close analogy to the very first discovery of quasicrystals using electron diffraction. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. These measurements pave the way for quantum simulations in fractal structures and higher dimensions. arXiv:1807.00823v2 [cond-mat.quant-gas]

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“…Quasicrystals do not show periodicity and have no long range translational symmetry. Yet they present longrange order and have a well-defined Bragg diffraction pattern [41][42][43][44][45][46][47]. The diffraction patterns from quasicrystal lattices reveal fivefold, eightfold and tenfold symmetries that cannot originate from a periodic arrangement of unit cells.…”

Section: Introductionmentioning

confidence: 99%

Quantum percolation in quasicrystals using continuous-time quantum walk

2019

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We study the percolation of a quantum particle on quasicrystal lattices and compare it with the square lattice. For our study, we have considered quasicrystal lattices modelled on the pentagonally symmetric Penrose tiling and the octagonally symmetric Ammann-Beenker tiling. The dynamics of the quantum particle are modelled using the continuous-time quantum walk (CTQW) formalism. We present a comparison of the behaviour of the CTQW on the two aperiodic quasicrystal lattices and the square lattice when all the vertices are connected and when disorder is introduced in the form of disconnections between the vertices. Unlike on a square lattice, we see a significant fraction of the quantum state localized around the origin in the quasicrystal lattices. With increase in disorder, the percolation probability of a particle on a quasicrystal lattice decreases significantly faster when compared to the square lattice. This study also sheds light on the fraction of disconnections allowed to see percolation of quantum particle on these quasicrystal lattices.

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Quasicrystals: What do we know? What do we want to know? What can we know?

Cited by 97 publications

References 77 publications

Mean-field phases of an ultracold gas in a quasicrystalline potential

Mean-field phases of an ultracold gas in a quasicrystalline potential

Matter-Wave Diffraction from a Quasicrystalline Optical Lattice

Quantum percolation in quasicrystals using continuous-time quantum walk

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