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arXiv:1511.07593 · Physical Review A

Moiré superlattice structures in kicked Bose-Einstein condensates

L. ORiordan, Angela White, Thomas Busch

Published Feb 4, 2016• 21 citations
arXivHTMLPDF

Abstract

Vortex lattices in rapidly rotating Bose-Einstein condensates lead to a periodic modulation of the superfluid density with a triangular symmetry. Here we show that this symmetry can be combined with an external perturbation in order to create superlattice structures with two or more periodicities. Considering a condensate that is kicked by an optical lattice potential, we find the appearance of transient moir\'e lattice structures, which can be identified using the kinetic energy spectrum.

DOI
10.1103/physreva.93.023609

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Vortex lattices in rapidly rotating Bose-Einstein condensates lead to a periodic modulation of the superfluid density with a triangular symmetry. Here we show that this symmetry can be combined with an external perturbation in order to create superlattice structures with two or more periodicities. Considering a condensate that is kicked by an optical lattice potential, we find the appearance of transient moir'e lattice structures, which can be identified using the kinetic energy spectrum.
We investigate the Moiré superlattice structures generated by the interplay between vortex lattice and optical lattice in two-component Bose–Einstein condensates. Square vortex lattices are generated in both components of the rapidly rotating condensates, and an optical lattice with the same geometry as the vortex lattice is acted on the condensates for a short interval. The optical lattice provides a sudden phase imprint, leading to the appearance of a transient phonon lattice. Such lattice, combined with vortex lattice and twisted an angle from each other, results in the generation of transient Moiré superlattice. The possible superlattice patterns under different twist angles are studied, and the corresponding vertex spacing is determined. We also study the relative shift of the Moir é superlattices in two components of the condensates and give the corresponding shift vector. Our results enrich the quantum phases in cold atomic systems, and contribute to the understanding of Moiré physics in these systems.
This body of work examines the non-equilibrium dynamics of vortex lattice carrying Bose–Einstein condensates. We solve the mean-feld Gross–Pitaevskii equation for a two-dimensional pancake geometry, in the co-rotating frame within the limit of high rotation frequencies. The condensate responds to this by creating a large periodic lattice of vortices with 6-fold triangular symmetry. By applying two distinct perturbations to this lattice, we examine the resulting effects on the vortices during time evolution. The frst perturbation involves applying an optical potential with matching geometry to the vortex lattice. We observe the appearance of interference fringes, and we show that these can be described by moiré interference theory. This is backed up by a decomposition of the kinetic energy spectra of the condensate. The applied perturbation only modifes the condensate density, with the vortex positions largely unaffected. From this we conclude that the vortex lattice is very stable and robust against phononic disturbances. Next, by removing vortices at predefned positions in the lattice using phase imprinting techniques, we examine the resulting order of the lattice. By performing this we generate stable topological defects in the crystal structure. The resulting lattice remains highly ordered in the presence of low numbers of these defects, where crystal structure and order of the lattice shows to be highly robust. By varying the type of imprinted phases we can create controllable degrees of disorder in the lattice. This disorder is analysed using orientational correlations, Delaunay triangulation, and Voronoi diagrams of the vortex lattice, and demonstrates a method for examining order and generating disorder in vortex lattices in Bose–Einstein condensates. All work described makes extensive use of GPU computing techniques, and allows for the simulation of these systems to be realised in short times. The implementation of the calculations using GPU computing are also discussed, where the software is shown to be the fastest of its kind out of the independently tested software suites.
Moiré superlattices, a twisted functional structure crossing the periodic and nonperiodic potentials, have recently attracted great interest in multidisciplinary fields, including optics and ultracold atoms, because of their unique band structures, physical properties, and potential implications. Driven by recent experiments on quantum phenomena of bosonic gases, the atomic Bose–Einstein condensates in moiré optical lattices, by which other quantum gases such as ultracold fermionic atoms are trapped, could be readily achieved in ultracold atom laboratories, whereas the associated nonlinear localization mechanism remains unexploited. Here, we report the nonlinear localization theory of ultracold atomic Fermi gases in two-dimensional moiré optical lattices. The linear Bloch-wave spectrum of such a twisted structure exhibits rich nontrivial flat bands, which are separated by different finite bandgaps wherein the existence, properties, and dynamics of localized superfluid Fermi gas structures of two types, gap solitons and gap vortices (topological modes) with vortex charge S=1, are studied numerically. Our results demonstrate the wide stability regions and robustness of these localized structures, opening up a new avenue for studying soliton physics and moiré physics in ultracold atoms beyond bosonic gases.
Moiré superlattices, classified as a supercell periodic structure configured from a periodic lattice overlaps with its twisted counterpart, have been demonstrated to exhibit many emergent linear and nonlinear phenomena like moiré induced flat bands, unconventional superconductivity, unique linear classical wave localization and nonlinear localized modes. Recent studies are, however, mainly focused on twisted bilayer structures, the static and nonequilibrium physics of trilayer moiré superlattices have remained largely unknown. We here consider trilayer moiré optical lattices by which Bose−Einstein condensates are trapped, and demonstrate theoretically the emergent flat bands and nonlinear phenomena — localized gap modes in form of gap solitons and vortices with a topological charge s=1. We give a unified picture for constructing optimal (largest) photonic forbidden gaps in such trilayer moiré superlattices and reveal nonlinear localization mechanism therein. Computational studies demonstrated the robustness of these localized modes, enabling insightful inspections of moiré physics and exploring ongoing moiré photonics applications in twisted trilayer superlattices in optics and ultracold atoms.
We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates. Vortices are pinned to columnar pinning sites created by a corotating optical lattice superimposed on the rotating Bose-Einstein condensates. We study the effects of two types of optical lattice: triangular and square. In both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural crossover in the vortex lattice.