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Emergence of Order from Turbulence in an Isolated Planar Superfluid

Tapio Simula, Matthew J. Davis, and Kristian Helmerson
Phys. Rev. Lett. 113, 165302 – Published 17 October 2014
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    Abstract

    We study the relaxation dynamics of an isolated zero temperature quasi-two-dimensional superfluid Bose-Einstein condensate that is imprinted with a spatially random distribution of quantum vortices. Following a period of vortex annihilation the remaining vortices self-organize into two macroscopic coherent “Onsager vortex” clusters that are stable indefinitely—despite the absence of driving or external dissipation in the dynamics. We demonstrate that this occurs due to a novel physical mechanism—the evaporative heating of the vortices—that results in a negative-temperature phase transition in the vortex degrees of freedom. At the end of our simulations the system is trapped in a nonthermal state. Our computational results provide a pathway to observing Onsager vortex states in a superfluid Bose gas.

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    • Received 13 May 2014

    DOI:https://doi.org/10.1103/PhysRevLett.113.165302

    © 2014 American Physical Society

    Authors & Affiliations

    Tapio Simula1, Matthew J. Davis2, and Kristian Helmerson1

    • 1School of Physics, Monash University, Victoria 3800, Australia
    • 2School of Mathematics and Physics, University of Queensland, Queensland 4072, Australia

    See Also

    Vortex Gyroscope Imaging of Planar Superfluids

    A. T. Powis, S. J. Sammut, and T. P. Simula
    Phys. Rev. Lett. 113, 165303 (2014)

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    Vol. 113, Iss. 16 — 17 October 2014

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    • Figure 1
      Figure 1

      Onsager vortex formation in the Gross-Pitaevskii model. (a)–(f) Time series of the condensate column density. The location of vortices with positive and negative circulations are shown using blue (dark) and green (light) circles, respectively, and the white line indicates the vortex dipole moment vector d as defined in the text. The initial random vortex configuration in (a) evolves to the Onsager vortices configuration in (f) characterized by two large-scale, coherent clusters of vortices in a background field of sound. (g) The total number of vortices, N, as a function of time, with the dashed vertical lines indicating the times at which we plot the condensate density in (a)–(f). (h) Kinetic energy, E, of the system. (i) Dipole moment, d, of the vortex configuration as a function of time. In (g)–(i) the thin (red) curves correspond to instantaneous values and the thick smooth (blue) curves are sliding averages over a window of 15τ to smooth out rapid fluctuations. The bar under (d) shows the scale of condensate density and the length of the scale bar under (f) is 56aosc, the diameter of the trap.

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    • Figure 2
      Figure 2

      A schematic plot of entropy versus energy for the point-vortex model. A zero-entropy Bose-Einstein condensate forms at T=0+ with its negative-temperature counterpart, an Einstein-Bose condensate (EBC) [48], emerging at T=0−. Entropy is maximized at T=±∞ in the entropy-dominated normal state (NS), which has a stochastic distribution of vortices. The vortex binding-unbinding phase transition separates the normal state from the pair-collapse (PC) state at positive temperature, whereas there is a transition to the coherent Onsager vortex state at a vortex-number-dependent negative temperature.

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    • Figure 3
      Figure 3

      Point-vortex dynamics with the addition of vortex pair annihilation. (a) Vortex number, N, (b) energy, E, and (c) dipole moment, d, as functions of time for an ensemble of 500 simulations with an initial energy corresponding to that of the GPE simulation. Thick, smooth (blue) lines are ensemble averages, thin (red) curves are results from a typical single trajectory, and background (grey scale) densities are normalized histograms of the simulation ensemble. The slow undulations of the dipole moment in (c) are due to the large-scale orbital motion of the Onsager vortices.

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