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Bidirectional dynamic scaling in an isolated Bose gas far from equilibrium

Nature Physics volume 17, pages 457–461 (2021)Cite this article

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Abstract

Understanding and classifying non-equilibrium many-body phenomena, analogously to the classification of equilibrium states of matter into universality classes1,2, is an outstanding problem in physics. From stellar matter to financial markets, any many-body system can be out of equilibrium in a myriad of ways, and many are difficult to experiment on. It is therefore a major goal to establish universal principles that apply to different phenomena and physical systems. For equilibrium states, the universality seen in the self-similar spatial scaling of systems close to phase transitions lies at the heart of their classification. Recent theoretical work3,4,5,6,7,8,9,10,11,12,13,14 and experimental evidence15,16 suggest that isolated many-body systems far from equilibrium generically exhibit dynamic (spatiotemporal) self-similar scaling, akin to turbulent cascades17 and the Family–Vicsek scaling in classical surface growth18,19. Here we observe bidirectional dynamic scaling in an isolated quench-cooled atomic Bose gas; as the gas thermalizes and undergoes Bose–Einstein condensation, it shows self-similar net flows of particles towards the infrared (smaller momenta) and energy towards the ultraviolet (smaller length scales). For both infrared and ultraviolet dynamics we find that the scaling exponents are independent of the strength of the interparticle interactions that drive the thermalization.

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Fig. 1: Bidirectional thermalization in an isolated gas.
Fig. 2: Self-similar scaling dynamics.
Fig. 3: Universality for different interaction strengths.
Fig. 4: Quasi-condensation and phase ordering.

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Data availability

The data that support the findings of this study are available in the Apollo repository (https://doi.org/10.17863/CAM.53984). Any additional information is available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank J. Berges, T. Gasenzer, J. Schmiedmayer, M. K. Oberthaler, E. A. Cornell, V. Kasper and N. Navon for discussions. This work was supported by EPSRC (grants EP/N011759/1 and EP/P009565/1), ERC (QBox) and a QuantERA grant (NAQUAS, EPSRC grant EP/R043396/1). C.E. acknowledges support from Jesus College (Cambridge). T.A.H. acknowledges support from the EU Marie Skłodowska-Curie programme (grant MSCA-IF-2018 840081). R.P.S. acknowledges support from the Royal Society. Z.H. acknowledges support from the Royal Society Wolfson Fellowship.

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Authors and Affiliations

  1. Cavendish Laboratory, University of Cambridge, Cambridge, UK

    Jake A. P. Glidden, Christoph Eigen, Lena H. Dogra, Timon A. Hilker & Zoran Hadzibabic

  2. Clarendon Laboratory, University of Oxford, Oxford, UK

    Robert P. Smith

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Contributions

J.A.P.G. led the project. L.H.D. and C.E. contributed significantly to data collection, analysis, and production of figures. All authors contributed extensively to interpretation of the data and production of the manuscript.

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Correspondence to Jake A. P. Glidden or Zoran Hadzibabic.

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Extended data

Extended Data Fig. 1 Additional details of scaling procedure, for the a = 300 a0 data shown in Fig. 2 in the main text.

a-c, Infrared scaling dynamics on log-log axes. Panels a and b correspond to the top and bottom panel, respectively, in Fig. 2c in the main text. In c we illustrate partial collapse, with α = 1.15 and β = 0, to show more clearly how much the distribution moves along the k axis. d, Overview of scaling exponent probability densities for both infrared (IR) and ultraviolet (UV).

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Glidden, J.A.P., Eigen, C., Dogra, L.H. et al. Bidirectional dynamic scaling in an isolated Bose gas far from equilibrium. Nat. Phys. 17, 457–461 (2021). https://doi.org/10.1038/s41567-020-01114-x

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