Research Article

Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip

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Science  20 Dec 2019:
Vol. 366, Issue 6472, pp. 1480-1485
DOI: 10.1126/science.aaw9229
  • Fig. 1 Laser initialization of vortex clusters.

    (A) Experimental setup. A balanced homodyne detection scheme is implemented within a fiber interferometer. FBS, fiber beam splitter; PD, photodetector. Inset shows a scanning electron microscope image of the microtoroidal optical cavity used in the experiments. Scale bar, 20 μm. (B) Sketch of the vortex generation process. Laser heating of the microtoroid perimeter causes superfluid evaporation, followed by superflow (36). The flow exceeds the superfluid critical velocity at the top of the microtoroid pedestal, seeding the generation of vortex pairs. (C) Exemplar simulated metastable distributions showing the effects of vortex annihilation and of changes in total kinetic energy K and angular momentum L. The color map indicates the free-vortex probability density, with a maximum of pmax = {0.035, 0.075, 0.023, 0.12} μm−2, respectively, for the top to bottom metastable states. Top metastable state: {N,K,L} = {10,0.43 aJ, 120 ag μm2 s–1}; second to top: N → 9; second to bottom: K → 0.41 aJ; and bottom: L → 44 ag μm2 s–1.

  • Fig. 2 Interactions between vortices and third-sound on a disk.

    (A) Top left: Free vortices (blue) and pinned circulation (red) on the bottom surface of the microtoroid. Bottom left: A third-sound mode on the same surface. The vortices and third-sound couple due to the superposition of their flow fields, shown on the right for the case of a single vortex (blue dot) offset from the disk origin by distance r. Here, the surface color represents the third-sound mode amplitude profile and the blue lines are vortex streamlines. Confinement within the same microscale domain enhances both the interaction rate between vortices and third-sound and the resulting frequency splitting between counterpropagating third-sound modes. (B) Normalized splitting per vortex for third-sound modes (m,n) = (1,3), (1,5), and (1,8) calculated by finite-element modeling using the techniques detailed in (40) and outlined in section 2.1 of (32), with their respective spatial profiles. The inset schematically depicts the vortex-induced splitting Δf between clockwise and counterclockwise third-sound modes in the presence of a clockwise vortex, which would be observed as a function of frequency f in the power spectral density (PSD) of the optically measured superfluid motion.

  • Fig. 3 Temporal dynamics of third-sound splitting.

    (A) Vortex-dipole decay process. Red indicates quantized circulation around the pedestal reduces due to annihilation events. Light blue indicates orbiting free-vortex cluster spirals toward the origin due to dissipation. Dissipation is exaggerated for clarity. (B) Experimental splitting observed in the PSD of the (m,n) = (1,7) third-sound mode pair immediately after vortex-dipole initialization. Gray spectra are the third-sound mode pair without vortices. The residual splitting in these unperturbed spectra is caused by irregularities in the circularity of the microtoroid that break the degeneracy between standing-wave Bessel modes (31) and is accounted for in data processing [see section 1.3 of (37)]. f is the frequency of superfluid motion; f¯m is the mean resonance frequency of third-sound mode pair. (C) Temporal decay of splitting of the (m,n) = (1,8), (1,7), (1,5), (1,4), and (1,3) third-sound modes (top to bottom traces, respectively). These specific modes were chosen because of the high signal-to-noise ratio of their PSDs. The raw data were recorded on a high-bandwidth, high-memory-depth oscilloscope. Six continuous measurements were taken, separated by ~10-s data-saving periods. Colored circles at the start of each trace show the theoretical splitting of each third-sound mode pair for the best-fit initial vortex metastable distribution. Insets show spatial amplitude profiles of each third-sound mode.

  • Fig. 4 Single-shot evolution of vortex-cluster metastable states.

    (A) Evolution of total kinetic energy (blue curve) and free-vortex cluster kinetic energy (red curve). Insets show metastable vortex probability densities at times indicated by the vertical dashed lines. These probability densities have the same color scale as those in Fig. 1C, with pmax = {0.0087, 0.015, 0.032} μm−2, respectively, from left to right. The second and third metastable distributions are taken, respectively, just before and just after the 7-to-6 annihilation event. The angular momentum of each distribution is chosen, within the uncertainty window of the fit, to maximize the entropy of the state and therefore represents the most statistically likely of the experimentally plausible distributions. (B) Experimentally determined decay of the vortex number. Vertical dashed lines correspond to times in (A). Note that although these data display steps in the vortex number, this is a feature of our analysis that minimizes the root-mean-square uncertainty only over discrete vortex number. Our experiments approach single-vortex resolution; however, the continuous variation of vortex-induced splitting with time precludes direct unambiguous observation of individual steps in the splitting that result from creation or annihilation (40). (C and D) Point-vortex simulations of the system evolution [see section 3.3 of (37) for implementation]. (C) Evolution of the total (blue curve) and free-vortex (red curve) kinetic energies. (D) Evolution of the free-vortex number. In all traces, the shaded area corresponds to a 1-SD uncertainty.

Supplementary Materials

  • Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip

    Yauhen P. Sachkou, Christopher G. Baker, Glen I. Harris, Oliver R. Stockdale, Stefan Forstner, Matthew T. Reeves, Xin He, David L. McAuslan, Ashton S. Bradley, Matthew J. Davis, Warwick P. Bowen

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods 
    • Figs. S1 to S16
    • Table S1
    • References 

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