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Onset of a modulational instability in trapped dipolar Bose-Einstein condensates

Igor Ferrier-Barbut, Matthias Wenzel, Matthias Schmitt, Fabian Böttcher, and Tilman Pfau
Phys. Rev. A 97, 011604(R) – Published 25 January 2018
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    Abstract

    We explore the phase diagram of a finite-sized dysprosium dipolar Bose-Einstein condensate in a cylindrical harmonic trap. We monitor the final state after the scattering length is lowered from the repulsive BEC regime to the quantum droplet regime. Either an adiabatic transformation between a BEC and a quantum droplet is obtained or, above a critical trap aspect ratio λc=1.87(14), a modulational instability results in the formation of multiple droplets. This is in full agreement with the predicted structure of the phase diagram with a crossover region below λc and a multistable region above. Our results provide the missing piece connecting the previously explored regimes resulting in a single or multiple dipolar quantum droplets.

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    • Received 20 November 2017

    DOI:https://doi.org/10.1103/PhysRevA.97.011604

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Bose-Einstein condensatesCold atoms & matter wavesDipolar gasesFlow instabilityInteractions in fluidsInterparticle interactions
    Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsFluid DynamicsGeneral PhysicsStatistical Physics & Thermodynamics

    Authors & Affiliations

    Igor Ferrier-Barbut, Matthias Wenzel, Matthias Schmitt, Fabian Böttcher, and Tilman Pfau

    • 5. Physikalisches Institut and Center for Integrated Quantum Science and Technology IQST, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

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    Vol. 97, Iss. 1 — January 2018

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    Images

    • Figure 1
      Figure 1

      Phase diagram for a cylindrically trapped Dy164 BEC containing 6000 atoms, obtained with our experimental parameters: The z trapping frequency is fixed at ωz=2π×150Hz. The diagram is calculated with EGPE simulations. For λ below the critical point λ<λc shown as a diamond, the repulsive BEC and the quantum droplet states are connected through a crossover. Above the critical point there is a multistable region where both are stable (shown in gray). Lowering the scattering length with λ above the critical point leads to a modulational instability. Our experimental procedure to locate the critical aspect ratio λc is shown as arrows, where we have assumed abg=70a0. We vary λp, and two indicative paths are shown [λp=2.5 (through points 2 and 3) and λp=1.0 (through points 2′ and 3′)]; timings are indicated in the text. The vertical blue line and blue area represent the resulting experimental value and error of λc=1.87(14) (see text).

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    • Figure 2
      Figure 2

      Examples of final integrated density images resulting from different paths (identical within each row), indicated in the row. Imaging fringes are visible due to the size of the quantum droplet being smaller than our imaging resolution, and likely a slight displacement out of the focal plane. Misalignment of the objective caused a distortion of the images. The field of view in each image is 26μm×26μm.

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    • Figure 3
      Figure 3

      (a)–(f) PCA image decomposition examples, comparing two different paths: (a)–(c) for λp=2.55(10) and (d)–(f) for λp=1.80(7). (a) and (d) Raw images. (b) and (e) Decomposition of the raw image only on the first five eigenvectors. The result for λp=1.80 is very close to the raw image, while for λp=2.55 it is markedly different. (c) and (f) Decomposition over 100 eigenvectors. The field of view in each image is 26μm×26μm. (g) Comparing the average distribution of squared eigenvalues αl2 for four different paths. Below λp≈1.9 they are indistinguishable from each other, while above that value a clear difference is observed with more eigenvectors contributing.

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    • Figure 4
      Figure 4

      〈χ〉 as a function of λp. The average is obtained from over 50 images for each λp, and the values are normalized to the lowest λp. The standard deviation of χk is shown as a vertical error bar. The gray area represents the confidence interval of the extracted λc.

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