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  • Letter

Sieve of Eratosthenes for Bose-Einstein condensates in optical moiré lattices

Dmitry Kouznetsov, Pol Van Dorpe, and Niels Verellen
Phys. Rev. A 105, L021304 – Published 25 February 2022
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    Abstract

    We catalog known optical moiré lattices and uncover exotic lattice configurations following a geometric analog of the ancient sieve of Eratosthenes algorithm for finding prime numbers. Rich dynamics of Bose-Einstein condensates loaded into these optical lattices is revealed from numerical simulations of time-of-flight interference patterns. What sets this method apart is the ability to tune the periodicity of the optical lattices without changing the wavelength of the laser, yet maintaining the local potential at the individual lattice sites. In addition, we discuss the ability to spatially translate the optical lattice through applying a structured phase only.

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    • Received 23 September 2021
    • Accepted 11 February 2022

    DOI:https://doi.org/10.1103/PhysRevA.105.L021304

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Cold atoms & matter wavesCold gases in optical latticesGeometrical & wave opticsInterference & diffraction of lightOptical lattices & trapsQuasicrystalline structure
    1. Physical Systems
    Ultracold gases
    1. Techniques
    Abstract algebraMathematical physics methodsPattern formation
    Atomic, Molecular & OpticalInterdisciplinary PhysicsGeneral Physics

    Authors & Affiliations

    Dmitry Kouznetsov1,2, Pol Van Dorpe2,1, and Niels Verellen2

    • 1KU Leuven, Dept. of Physics and Astronomy, Research unit Quantum Solid-State Physics, B-3001 Leuven, Belgium
    • 2imec, Kapeldreef 75, B-3001 Leuven, Belgium

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    Issue

    Vol. 105, Iss. 2 — February 2022

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    Images

    • Figure 1
      Figure 1

      Generation of OLs using the integer lattice method. A planar laser beam configuration (a) is arranged such that the input beam orientations correspond to the concyclic points in the triangular integer lattice Z[ζ6] (b). The resulting interference pattern in the overlapping region of the input beams (c) shows a triangular symmetry.

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    • Figure 2
      Figure 2

      Integer lattice method classification of OLs analogous to the sieve of Eratosthenes algorithm. Each point in the diagram corresponds to a triangular (m=6) OL generated from an integer n. The distinction between lattices is based on lattice periodicity, with first occurring lattices Λ6 marked red and identical lattices marked gray. The trend lines of the periodicity are added as a visual aid (dashed lines). Noninert prime numbers P6 coincide with n of Λ6 (black squares). Higher-order moiré OLs (arrows) are generated from products of prime numbers, e.g., 91=7×13.

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    • Figure 3
      Figure 3

      Calculated matter-wave interference patterns corresponding to the momentum distribution of the superfluid in the OLs obtained using the integer lattice method (see Fig. 2). Each of the momentum distributions (a–f) shows different dynamics of the system, solely dependent on the choice of n. The dashed triangle (a–c) denotes the decrease of the first Brillouin zone, corresponding to more dense lattice sites. The parameters used in the calculations are ω=0.08,V0=−6, and g=10.

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    • Figure 4
      Figure 4

      Phase tuning scheme for spatial translation of the OL. A diagram of the phase shifts (a) for refocusing of the constructive interference of a system with three input beams (red dots) from point A to point B. The phase shift can be thought of as a displacement of the plane wave front: initial (gray lines) and displaced (black lines). Each phase shift has magnitude φj. Positive (orange bars) or negative (blue bars) phase shifts (b), when synchronized to follow a cardioid curve (dashed line), enable the spatial translation of the OL (c).

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