Direct observation of chiral currents and magnetic reflection in atomic flux lattices

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Science Advances  21 Apr 2017:
Vol. 3, no. 4, e1602685
DOI: 10.1126/sciadv.1602685
  • Fig. 1 Two-leg flux ladder.

    (A) Two sets of lattice laser fields (with wave numbers k1 and k2) addressing transitions between atomic momentum states of a Bose-Einstein condensate (BEC). (B) Free-particle dispersion relation showing momentum states on the m = 0 (white circles) and m = 1 (gray circles) legs, labeled by (m, n) with momentum p = 2(mk1 + nk2). Short red and tall blue arrows denote transitions controlled by k1 and k2 wave number lattices, respectively. Inset: 2D lattice representation, with links addressed by the k1 (red, vertical) and k2 (blue, horizontal) wave number beams. The recoil energy is given by Embedded Image. (C) Time-of-flight image of atoms in momentum orders (m, n). (D) Image from (C) rearranged to show the 2D lattice. This figure and (C) show absorption images using the normalized OD scale at the right. (E) Schematic of a two-leg ladder with applied tunneling phases φi on each link of the m = 1 leg, resulting in fluxes φi around each four-site plaquette. Max, maximum.

  • Fig. 2 Shearing in the flux ladder.

    (A) Schematic showing atoms undergoing clockwise shear (arrows) for positive flux φ, corresponding to an effective magnetic field B directed out of the page. Red filled-in circles represent the initial state. (B) Shearing dynamics for φ = −π/2 (top, blue) and φ = +π/2 (bottom, red). Dashed and solid curves represent numerical simulation results based on Eq. 1 and a more complete model taking into account off-resonant transitions, respectively, both scaled and offset to match the data. Dashed vertical lines indicate the time when the data for (C) and (D) were taken. (C) Site populations for φ = −π/2 (left, blue) and φ = +π/2 (right, red). Color scale used is the same as in Fig. 1D. (D) Shearing versus applied flux. Solid line represents results from a simulation of the more complete model. Measurements for (C) and (D) were taken after 500 μs (~1.06 /t), indicated by dashed vertical lines in (B). The calibrated tunneling rates for (B) and (D) are slightly different, so this time translates into different tunneling times for the two. All error bars denote 1 SE.

  • Fig. 3 Magnetic reflection.

    (A) Schematic depicting the lattice divided into two regions of different fluxes: 0 (unshaded, left) and φ (shaded, right). Population begins at the red filled-in lattice site. (B) Fraction of initial population transmitted into the shaded φ flux region as a function of φ after 1500-μs evolution time (~2.94 /t). Solid curve represents a numerical simulation with an overall scaling factor of 0.48 to fit the data. (C and D) Dynamics for (C) φ = 0 and (D) φ = π. Top: Integrated (over the image dimension normal to the lattice) OD images versus evolution time for data (left) and simulation (right, Sim). Leftmost red marker denotes initial site, and gray shaded markers denote shaded φ region. Bottom: Population in the zero-flux region (darker squares) and shaded φ region (open lighter circles) as a function of evolution time. Calibrated tunneling time [/t = 462(28) μs] for these dynamics differs from that of (B), and solid simulation curves account for an identical scaling as in (B). All error bars denote 1 SE.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. 2D lattice implementation.
    • fig. S2. Phase instability.
    • fig. S3. Nonzero initial shearing.
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