The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a superquasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials.
The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a superquasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials.
Deterministic quasiperiodicity in quantum systems has long been associated with localization, criticality, or glassy behavior, and has therefore been believed to suppress long-range order rather than stabilize it. Here we demonstrate the opposite: quasiperiodicity in interactions--without any quasiperiodic potential, disorder, or geometric modulation--can generate coherent, ordered quantum phases. We study hard-core bosons in one dimension with quasiperiodic long-range interactions, V_{ij}=V_0 \cos(παi)\cos(παj), where n=α=(\sqrt{5}-1)/2 is the inverse golden ratio. Using large-scale path-integral quantum Monte Carlo simulations, we uncover thermodynamically stable incompressible plateaus at irrational densities tied to Fibonacci ratios. These plateaus exhibit sharp incommensurate Bragg peaks, signaling an emergent quasi-solid with long-range quasicrystalline density order. More strikingly, at nearby fillings and interaction strengths, we identify a quasi-supersolid phase that supports both Fibonacci density ordering and finite superfluid density--demonstrating that interaction-induced quasiperiodicity can stabilize supersolid coherence. Our results establish a new mechanism for realizing ordered quasicrystalline quantum matter, and provide realistic guidance for implementation in Rydberg atom arrays, multimode cavity-QED systems, and trapped-ion quantum simulators.
Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases under these long-range interactions. In this work, we study repulsive ultracold dipolar fermions in a quasiperiodic optical lattice to characterize the behavior of interacting quasicrystals. We simulate the full time evolution of the typical experimental protocols used to probe quasicrystalline order and localization properties. We extract experimentally measurable dynamical observables and correlation functions to characterize the three phases observed in the noninteracting setting: localized, intermediate, and extended. We then study the stability of such phases to repulsive dipolar interactions. We find that dipolar interactions can completely alter the shape of the phase diagram by stabilizing the intermediate phase, mostly at the expense of the extended phase. Moreover, in the strongly interacting regime, a resonance-like behavior characterized by density oscillations appears. Remarkably, strong dipolar repulsions can also localize particles even in the absence of quasiperiodicity if the primary lattice is sufficiently deep. Our work shows that dipolar interactions in a quasiperiodic potential can give rise to a complex, tunable coexistence of localized and extended quantum states.
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, self-similarity, and the presence of non-trivial structure on all scales. The concept of aperiodic order has been extensively studied in mathematics and geometry, exemplified by the celebrated Penrose tiling. However, the understanding of physical quasicrystals (the vast majority of them are intermetallic compounds) is still incomplete owing to their complexity, regarding both growth processes and stability. Ultracold atoms in optical lattices offer an ideal, yet untested environment for investigating quasicrystals. Optical lattices, i.e. standing waves of light, allow the defect-free formation of a large variety of potential landscapes, including quasiperiodic geometries. In recent years, optical lattices have become one of the most successful tools in the large-scale quantum simulation of condensed-matter problems. This study presents the first experimental realisation of a two-dimensional quasicrystalline potential for ultracold atoms, based on an eightfold symmetric optical lattice. It is aimed at bringing together the fields of ultracold atoms and quasicrystals – and the more general concept of aperiodic order. The first part of this thesis introduces the theoretical aspects of aperiodic order and quasicrystalline structure. The second part comprises a detailed account of the newly designed apparatus that has been used to produce quantum-degenerate gases in quasicrystalline lattices. The third and final part summarises the matter-wave diffraction experiments that have been performed in various lattice geometries. These include one- and two-dimensional simple cubic lattices, one-dimensional quasiperiodic lattices, as well as two-dimensional quasicrystalline lattices. The striking self-similarity of this quasicrystalline structure has been directly observed, in close analogy to Shechtman’s very first discovery of quasicrystals using electron diffraction. In addition, an in-depth study of the diffraction dynamics reveals the fundamental differences between periodic and quasicrystalline lattices, in excellent agreement with ab initio theory. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. On the one hand, these measurements establish a novel experimental platform for investigating quasicrystals proper. On the other hand, ultracold atoms in quasicrystalline optical lattices are worth studying in their own right: Possible avenues include the observation many-body localisation and Bose glasses, as well as the creation of topologically non-trivial systems in higher dimensions.
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.
We study the emergence of quasicrystal configurations in the ground-state phase diagram of bosonic systems interacting through pair potentials of Lifshitz's type. By using a variational mean-field approach, we determine the relevant features of the corresponding potential interaction kind stabilizing such quasicrystalline states in two dimensions. Unlike their classical counterpart, in which the interplay between only two wave vectors determines the resulting symmetries of the solutions, the quantum picture relates in a more complex way to the instabilities of the excitation spectrum. Moreover, the quantum quasicrystal patterns are found to emerge as the ground state with no need of moderate thermal fluctuations. The study extends to the exploration of the excitation properties and the possible existence of superquasicrystals, i.e., supersolidlike quasicrystalline states in which the long-range nonperiodic density profile coexists with a nonzero superfluid fraction. Our calculations suggest that, in an intermediate region between the homogeneous superfluid and the normal quasicrystal phases, these exotic states indeed exist at zero temperature. Comparison with full numerical simulations provides a solid verification of the variational approach adopted in this paper.