Revealing the Topology of Quasicrystals with a Diffraction Experiment

Quasicrystalline Bose Glass in the Absence of Disorder and Quasidisorder

We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact path integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate that develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects, particle interactions and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.

Superconductivity and strong interactions in a tunable moiré quasicrystal

Electronic states in quasicrystals generally preclude a Bloch description1, rendering them fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are underexplored relative to periodic and amorphous structures. Here we introduce a new type of highly tunable quasicrystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two mutually incommensurate moiré patterns. In contrast to many common atomic-scale quasicrystals2,3, the quasiperiodicity in our system is defined on moiré length scales of several nanometres. This 'moiré quasicrystal' allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Notably, in the quasiperiodic regime, we observe superconductivity near a flavour-symmetry-breaking phase transition4,5, the latter indicative of the important role that electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems but may also provide insights into electronic ordering in related periodic moiré crystals6-12. We anticipate that extending this platform to engineer quasicrystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasicrystals.

Hofstadter butterfly and topological edge states in a quasiperiodic photonic crystal cavity array

Quasiperiodic structures with additional synthetic degrees of freedom have recently been recognized as a promising way for investigating high-dimensional topological phases with lower physical dimensions. Here, we investigated the well-known Harper-Aubry-André model on an integrated photonic platform by proposing a new design of a quasiperiodic photonic crystal (PhC) cavity array. This array is composed of closely coupled H1 PhC cavities with their cavity lengths being periodically modulated in the real space. The frequency spectrum of the structure shows the main features of the Hofstadter butterfly, which is one of the most important phenomena in the Harper-Aubry-André model. By varying the modulation phase, this structure exhibits nontrivial topology, which supports strongly localized topological edge states. These results have shown that quasiperiodic PhC cavity arrays can serve as the testbed for studying topological phases and new topological phenomena on an integrated platform.

Strongly Interacting Bosons in a Two-Dimensional Quasicrystal Lattice

Quasicrystals exhibit exotic properties inherited from the self-similarity of their long-range ordered, yet aperiodic, structure. The recent realization of optical quasicrystal lattices paves the way to the study of correlated Bose fluids in such structures, but the regime of strong interactions remains largely unexplored, both theoretically and experimentally. Here, we determine the quantum phase diagram of two-dimensional correlated bosons in an eightfold quasicrystal potential. Using large-scale quantum Monte Carlo calculations, we demonstrate a superfluid-to-Bose glass transition and determine the critical line. Moreover, we show that strong interactions stabilize Mott insulator phases, some of which have spontaneously broken eightfold symmetry. Our results are directly relevant to current generation experiments and, in particular, drive prospects to the observation of the still elusive Bose glass phase in two dimensions and exotic Mott phases.

Actively controlled asymmetric edge states for directional wireless power transfer

Wireless power transfer (WPT) has triggered immense research interest in a range of practical applications, including mobile phones, logistic robots, medical-implanted devices and electric vehicles. With the development of WPT devices, efficient long-range and robust WPT is highly desirable but also challenging. In addition, it is also very important to actively control the transmission direction of long-range WPT. Recently, the rise of topological photonics provides a powerful tool for near-field robust control of WPT. Considering the technical requirements of robustness, long-range and directionality, in this work we design and fabricate a one-dimensional quasiperiodic Harper chain and realize the robust directional WPT using asymmetric topological edge states. Specially, by further introducing a power source into the system, we selectively light up two Chinese characters, which are composed of LED lamps at both ends of the chain, to intuitively show the long-range directional WPT. Moreover, by adding variable capacitance diodes into the topological quasiperiodic chain, we present an experimental demonstration of the actively controlled directional WPT based on electrically controllable coil resonators. With the increase in voltage, we measure the transmission at two ends of the chain and observe the change of transmission direction. The realization of an actively tuned topological edge states in the topological quasiperiodic chain will open up a new avenue in the dynamical control of robust long-range WPT.

Matter-Wave Diffraction from a Quasicrystalline Optical Lattice

Quasicrystals are long-range ordered and yet nonperiodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of nontrivial structure on all scales. Here, we report on the first experimental demonstration of an eightfold rotationally symmetric optical lattice, realizing a two-dimensional 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.

Topological bands for ultracold atoms

There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, descriptions are given of the forms of interparticle interactions that emerge when atoms are subjected to these energy bands and of some of the many-body phases that may be sought in future experiments.

Asymmetric topological edge states in a quasiperiodic Harper chain composed of split-ring resonators

Quasiperiodic structures have recently been found to possess salient topological properties. In this Letter, we theoretically and experimentally demonstrate the topological edge states in a quasiperiodic Harper chain composed of split-ring resonators. In a finite-size Harper chain, we find that there is always a pair of edge states in the bandgaps, independent of the number of the resonators. Different from the topological edge states localized at both ends of a periodic chain, this pair of edge states is selectively localized at the left or right end of the quasiperiodic chain at different frequencies. These paired-edge states with asymmetric field distribution can be used for unidirectional propagation. Our results not only provide a versatile platform to study the topological physics beyond the periodic structures but also may be useful in some applications such as selective unidirectional power transfer.