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arXiv:2503.15359 · Physical review. B./Physical review. B

Engineering interaction potentials for stabilizing quantum quasicrystal phases

Matheus Grossklags, Daniel Lima, Vinicius Zampronio, Fabio Cinti, Alejandro Mendoza-Coto

Published Nov 14, 2025• 1 citation
arXivHTMLPDF

Abstract

We investigate the necessary features of the pair interaction for the stabilization of self-assembled quantum quasicrystals in two-dimensional bosonic systems. Unlike the classical scenario, our results show that two-dimensional octagonal, decagonal, and dodecagonal aperiodic phases require a distinct number of properly tuned characteristic length scales for their stabilization. By using a mean-field spectral variational approach and Gross-Pitaevskii numerical calculations, we determine that the dodecagonal quasicrystal structure requires at least two characteristic length scales for its stabilization, while the decagonal and octagonal patterns need at least three and four length scales, respectively. The family of pair interaction potentials considered, albeit simple, is well justified in terms of a novel experimental platform based on laser-painted interactions in a cavity QED setup. Finally, we perform a structural characterization of the quasicrystal patterns obtained and show that these phases coexist with a finite superfluid fraction, forming what can be called a super quasicrystal phase.

DOI
10.1103/vnt6-9g1l

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We investigate the necessary features of the pair interaction for the stabilization of self-assembled quantum quasicrystals in two-dimensional bosonic systems. Unlike the classical scenario, our results show that two-dimensional octagonal, decagonal, and dodecagonal aperiodic phases require a distinct number of properly tuned characteristic length scales for their stabilization. By using a mean-field spectral variational approach and Gross-Pitaevskii numerical calculations, we determine that the dodecagonal quasicrystal structure requires at least two characteristic length scales for its stabilization, while the decagonal and octagonal patterns need at least three and four length scales, respectively. The family of pair interaction potentials considered, albeit simple, is well justified in terms of a novel experimental platform based on laser-painted interactions in a cavity QED setup. Finally, we perform a structural characterization of the quasicrystal patterns obtained and show that these phases coexist with a finite superfluid fraction, forming what can be called a super quasicrystal phase.
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.
Quantum quasicrystals, characterized by aperiodic order, exhibit unique low-energy excitations such as phononic, phasonic, and hybridized modes, making them a focal point for studying symmetry-driven dynamics in ultracold atomic systems. Understanding these excitations and phase transitions is crucial for advancing quantum simulation technologies. This study investigates the role of quasicrystal symmetry (octagonal, decagonal, and dodecagonal) in determining anisotropic excitation behaviors and phase stability, validating theoretical predictions through simulated ultracold atom experiments. Using the Gross-Pitaevskii equation and Bogoliubov-de Gennes linearization, we simulated Bose-Einstein condensates in quasiperiodic potentials, varying potential depth V0 from 0.5 to 4.0 arbitrary units. Excitation spectra were computed to assess anisotropy, and minimum frequencies at k=0 were analyzed to identify phase boundaries. Simulations were conducted using Python with NumPy, SciPy, and Matplotlib, visualizing dispersion relations and phase diagrams. Octagonal quasicrystals displayed anisotropic excitation spectra (frequencies 1.368–1.464), reflecting mode hybridization, while decagonal (1.413–1.453) and dodecagonal (1.696–1.736) systems showed more isotropic behaviors. Phase boundary analysis revealed persistent gaps (octagonal: 1.0–5.0, decagonal: 1.5–6.0, dodecagonal: 2.0–7.0), indicating no quasicrystal phase within the simulated V0 range, likely transitioning to superfluid or disordered states. Quasicrystal symmetry significantly influences excitation anisotropy and phase stability, with higher symmetries (dodecagonal) exhibiting larger gaps and reduced quasicrystal stability. Future studies should explore lower V0 ranges and incorporate temperature effects to locate the quasicrystal phase, enhancing experimental validation.
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.
A quantum quasicrystal was proposed to exist by mean-field, variational arguments in two-dimensional Rashba spin-orbit coupled BECs with dipolar interactions. Despite this remarkable prediction, there is little known about the superfluid character or stability of this quasicrystalline state against thermal and quantum fluctuations, whose importance is implied by the massive single-particle degeneracy of the Rashba Hamiltonian. Here, we apply field-theoretic numerical simulations based on a boson coherent state path integral representation to simulate the finite-temperature behavior of a periodic approximant of an octagonal quasicrystal. We find that the quasicrystal state maintains a 50% superfluid fraction down to low temperature, suggesting supersolid character. We compute a phase diagram that depicts a region of thermodynamic stability for the octagonal quasicrystal phase at low temperature. At intermediate temperature, the quasicrystal undergoes a first-order transition into a crystalline BEC with hexagonal symmetry. Our findings support a possible experimental realization of the octagonal quasicrystal in ^{164}Dy quantum gases below a temperature of 75 nK.
We study the emergence of Bose glass phases in self sustained bosonic quasicrystals induced by a pair interaction between particles of Lifshitz–Petrich type. By using a mean-field variational method designed in momentum space as well as Gross–Pitaevskii simulations we determine the phase diagram of the model. The study of the local and global superfluid fraction allows the identification of supersolid, super quasicrystal, Bose glass and insulating phases. The Bose glass phase emerges as a quasicrystal phase in which the global superfluidity is essentially zero, while the local superfluidity remains finite in certain ring structures of the quasicrystalline pattern. Furthermore, we perform continuous space Path Integral Monte Carlo simulations for a case in which the interaction between particles stabilizes a quasicrystal phase. Our results show that as the strength of the interaction between particles is increased the system undergoes a sequence of states consistent with the super quasicrystal, Bose glass, and quasicrystal insulator thermodynamic phases.
Quantum simulation of quasicrystals in synthetic bosonic matter now paves the way for the exploration of these intriguing systems in wide parameter ranges. Yet thermal fluctuations in such systems compete with quantum coherence and significantly affect the zero-temperature quantum phases. Here we determine the thermodynamic phase diagram of interacting bosons in a two-dimensional, homogeneous quasicrystal potential. We find our results using quantum Monte Carlo simulations. Finite-size effects are carefully taken into account and the quantum phases are systematically distinguished from thermal phases. In particular, we demonstrate stabilization of a genuine Bose glass phase against the normal fluid in sizable parameter ranges. We interpret our results for strong interactions using a fermionization picture and discuss experimental relevance.