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Order from chaos: Observation of large-scale flow from turbulence in a two-dimensional superfluid

Shaun Johnstone, Andrew J. Groszek, Philip T. Starkey, Billington, Christopher J., Tapio Simula, Kristian Helmerson

Published Jan 1, 2019• 67 citations
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Abstract

Interacting systems driven far from equilibrium tend to evolve to steady states exhibiting large-scale structure and order. In two-dimensional turbulent flow the seemingly random swirling motion of a fluid can evolve towards persistent large-scale vortices. Lars Onsager proposed a model based on statistical mechanics of quantized vortices to explain such behavior. Here we report the first experimental confirmation of Onsager's model of turbulence. We drag a grid barrier through an oblate superfluid Bose--Einstein condensate to generate non-equilibrium distributions of vortices. We observe an inverse energy cascade driven by the evaporative heating of vortices, leading to steady-state configurations characterized by negative temperatures. Our results open a pathway for quantitative studies of emergent structures in interacting quantum systems driven far from equilibrium.

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Nonequilibrium interacting systems can evolve to exhibit large-scale structure and order. In two-dimensional turbulent flow, the seemingly random swirling motion of a fluid can evolve toward persistent large-scale vortices. To explain such behavior, Lars Onsager proposed a statistical hydrodynamic model based on quantized vortices. Here, we report on the experimental confirmation of Onsager's model. We dragged a grid barrier through an oblate superfluid Bose-Einstein condensate to generate nonequilibrium distributions of vortices. We observed signatures of an inverse energy cascade driven by the evaporative heating of vortices, leading to steady-state configurations characterized by negative absolute temperatures. Our results open a pathway for quantitative studies of emergent structures in interacting quantum systems driven far from equilibrium.

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Onsager Vortices at Negative Temperatures

Tapio Simula, Rahil N. Valani, Philip T. Starkey +6 more

We have theoretically [1-5] and experimentally [6] studied statistical mechanics of vortices in two-dimensional superfluids in confined geometries. We are particularly interested in the part of the phase diagram where negative absolute temperature states of the vortex degrees of freedom are realized. The vortex dynamics is driven by two opposing mechanisms: a vortex evaporative heating due to vortex-antivortex annihilations drives the system toward low entropy negative temperature states while the coupling to the  phonon bath results in cooling of the vortices driving the system toward vortex dipole dominated positiver temperature states. Furthermore, we have observed, both theoretically and experimentally, signatures of anomalous dynamical scaling and evolution toward non-thermal fixed points. For sufficiently high energies the Onsager vortex clusters are predicted to undergo Einstein-Bose condensation - a negative temperature counterpart to the Berezinskii-Kosterlitz-Thouless transition. [1] T Simula, MJ Davis, K Helmerson, Emergence of Order from Turbulence in an Isolated Planar Superfluid , Physical Review Letters 113, 165302, (2014). [2] AJ Groszek, TP Simula, DM Paganin, K Helmerson, Onsager vortex formation in Bose-Einstein condensates in two-dimensional power-law traps, Physical Review A 93, 043614, (2016). [3] RN Valani, AJ Groszek, TP Simula, Einstein–Bose condensation of Onsager vortices , New Journal of Physics 20, 053038, (2018). [4] AJ Groszek, MJ Davis, DM Paganin, K Helmerson, TP Simula, Vortex thermometry for turbulent two-dimensional fluids, Physical Review Letters 120, 034504, (2018). [5] AJ Groszek, MJ Davis, TP Simula, Decaying quantum turbulence in a two-dimensional Bose-Einstein condensate at finite temperature , arXiv:1903.05528. [6] Shaun P Johnstone, Andrew J Groszek, Philip T Starkey, Christopher J Billington, Tapio P Simula, Kristian Helmerson, Order from chaos: Observation of large-scale flow from turbulence in a two-dimensional superfluid, arXiv:1801.06952.

StatPhys 27 Main Conference•May 15, 2019•0 citations
Interacting systems driven far from equilibrium tend to evolve to steady states exhibiting large-scale structure and order. In two-dimensional turbulent flow the seemingly random swirling motion of a fluid can evolve towards persistent large-scale vortices. Lars Onsager proposed a model based on statistical mechanics of quantized vortices to explain such behavior. Here we report the first experimental confirmation of Onsager's model of turbulence. We drag a grid barrier through an oblate superfluid Bose--Einstein condensate to generate non-equilibrium distributions of vortices. We observe an inverse energy cascade driven by the evaporative heating of vortices, leading to steady-state configurations characterized by negative temperatures. Our results open a pathway for quantitative studies of emergent structures in interacting quantum systems driven far from equilibrium.
Nonequilibrium interacting systems can evolve to exhibit large-scale structure and order. In two-dimensional turbulent flow, the seemingly random swirling motion of a fluid can evolve toward persistent large-scale vortices. To explain such behavior, Lars Onsager proposed a statistical hydrodynamic model based on quantized vortices. Here, we report on the experimental confirmation of Onsager's model. We dragged a grid barrier through an oblate superfluid Bose-Einstein condensate to generate nonequilibrium distributions of vortices. We observed signatures of an inverse energy cascade driven by the evaporative heating of vortices, leading to steady-state configurations characterized by negative absolute temperatures. Our results open a pathway for quantitative studies of emergent structures in interacting quantum systems driven far from equilibrium.
Lars Onsager noted that turbulent fluids constrained to flow in two dimensions tend to develop large-scale features. Quantum fluids, such as atomic Bose–Einstein condensates, also feature turbulent flows, however their vortices behave as discrete point-like particles. This thesis presents the results of experiments on the distribution of quantised vortices in highly oblate, uniform Bose-Einstein condensates. Initially randomly distributed vortices were observed to rearrange themselves to become more ordered, resembling Onsager’s description of large-scale flow features. These results add to our current understanding of the physical processes involved in turbulent flows of superfluids.
We have studied computationally turbulent non-equilibrium dynamics of quasi-two-dimensional superfluid Bose-Einstein condensates. Beginning with a random out-of-equilibrium distribution of vortices and antivortices in the condensate, we have observed emergence of ordered vortex structures corresponding to absolute negative temperature states in this conservative Hamiltonian system. We explain the spontaneous self-organization of the singly quantized vortices into two``Onsager vortex''clusters of like-signed vortices in terms of an``evaporative heating''mechanism of the vortex gas. These results provide a clear pathway to observing Onsager vortex structures and their unusual thermodynamics in a superfluid Bose gas
Turbulence in classical fluids is a ubiquitous non-equilibrium phenomenon, yet a complete theoretical description for turbulent flow remains a challenging problem. A useful simplification for ideal two-dimensional (2D) fluids is to describe the turbulent flow with long-range-interacting point vortices, each possessing quantised circulation. In 1949, Onsager applied statistical mechanics to determine the equilibria of this model. He showed that at sufficiently high energies, like-circulation vortices preferentially aggregate into large-scale clusters, and are characterised by a negative absolute temperature. Onsager's theory has been highly influential, providing understanding of diverse quasi-2D systems such as turbulent soap films, guiding-centre plasmas, and self-gravitating systems. It also predicts the striking tendency of 2D turbulence to spontaneously form large-scale, long-lived vortices -- Jupiter's Great Red Spot is a well-known example. However, Onsager's theory doesn't quantitatively apply to classical fluids where vorticity is continuous, and experimental systems demonstrating Onsager's point-vortex statistical mechanics have remained elusive. Here we realise high energy, negative-temperature vortex clusters in a uniform superfluid Bose-Einstein condensate. Our results confirm Onsager's prediction of negative temperature clustered phases of quantum vortices, and demonstrate the utility of point-vortex statistical mechanics in 2D quantum fluids. This work opens future directions for the study of turbulent dynamics and we anticipate exploring the entire phase diagram of 2D quantum vortices, including the formation of clusters from 2D quantum turbulence.
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.
We have theoretically [1-5] and experimentally [6] studied statistical mechanics of vortices in two-dimensional superfluids in confined geometries. We are particularly interested in the part of the phase diagram where negative absolute temperature states of the vortex degrees of freedom are realized. The vortex dynamics is driven by two opposing mechanisms: a vortex evaporative heating due to vortex-antivortex annihilations drives the system toward low entropy negative temperature states while the coupling to the  phonon bath results in cooling of the vortices driving the system toward vortex dipole dominated positiver temperature states. Furthermore, we have observed, both theoretically and experimentally, signatures of anomalous dynamical scaling and evolution toward non-thermal fixed points. For sufficiently high energies the Onsager vortex clusters are predicted to undergo Einstein-Bose condensation - a negative temperature counterpart to the Berezinskii-Kosterlitz-Thouless transition. [1] T Simula, MJ Davis, K Helmerson, Emergence of Order from Turbulence in an Isolated Planar Superfluid , Physical Review Letters 113, 165302, (2014). [2] AJ Groszek, TP Simula, DM Paganin, K Helmerson, Onsager vortex formation in Bose-Einstein condensates in two-dimensional power-law traps, Physical Review A 93, 043614, (2016). [3] RN Valani, AJ Groszek, TP Simula, Einstein–Bose condensation of Onsager vortices , New Journal of Physics 20, 053038, (2018). [4] AJ Groszek, MJ Davis, DM Paganin, K Helmerson, TP Simula, Vortex thermometry for turbulent two-dimensional fluids, Physical Review Letters 120, 034504, (2018). [5] AJ Groszek, MJ Davis, TP Simula, Decaying quantum turbulence in a two-dimensional Bose-Einstein condensate at finite temperature , arXiv:1903.05528. [6] Shaun P Johnstone, Andrew J Groszek, Philip T Starkey, Christopher J Billington, Tapio P Simula, Kristian Helmerson, Order from chaos: Observation of large-scale flow from turbulence in a two-dimensional superfluid, arXiv:1801.06952.