Abstract
Hydrodynamics is a successful framework for effectively describing the dynamics of complex many-body systems, ranging from subnuclear to cosmological scales. It applies coarse-grained assumptions about the microscopic constituents of a system to define macroscopic fluid cells, which are large compared to the interparticle spacing and mean free path. In high-energy heavy-ion collisions, hydrodynamic behaviour is inferred from the observation of elliptic flow, which is the elliptical deformation of the particle momentum distribution. Here we demonstrate the emergence of elliptic flow in a mesoscopic system with a few strongly interacting ultracold atoms. In our system, a hydrodynamic description is a priori not applicable, as all relevant length scales—the system size, the interparticle spacing and the mean free path—are comparable. The single-particle resolution and the deterministic control over the number of particles and interaction strength in our experiment allow us to explore the boundaries between a microscopic description and a hydrodynamic framework, and we show that elliptic flow appears as an interaction-driven effect. Our results demonstrate the emergence of collective behaviour in a regime where hydrodynamics is not usually applicable.
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Data availability
The data that support the findings in this study are available from the Zenodo repository, https://doi.org/10.5281/zenodo.11504182 (ref. 43). Source data are provided with this paper.
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Acknowledgements
We gratefully acknowledge insightful discussions with T. Enss, A. Mazeliauskas and J.-Y. Ollitrault. This work has been supported by the Heidelberg Center for Quantum Dynamics, the DFG Collaborative Research Centre SFB 1225 (ISOQUANT) (S.F. and S.J.), the DFG project DFG FL 736/3-1 (NEQFluids) (S.F.), Germany’s Excellence Strategy EXC2181/1-390900948 (Heidelberg Excellence Cluster STRUCTURES) (S.J.) and the European Union’s Horizon 2020 research and innovation programme (Grant Agreement Nos. 817482 (PASQuanS) and 725636 (ERC QuStA), both to S.J.). This work has been partially financed by the Baden-Württemberg Stiftung (P.M.P. and S.J.).
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S.B., P.L, C.H. and S.J conceived the experiment. S.B. and C.H. performed the measurements. P.L., S.B. and C.H. analysed the data. S.J. supervised the experimental part of the project. S.F., G.G. and L.H.H. set up and ran the hydrodynamic simulations. S.B. and P.L. wrote the paper with input from all authors. All authors contributed to the discussion of the results.
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Extended data
Extended Data Fig. 1 Initial system.
We prepare our initial system in a 2D harmonic oscillator. a The confinement is given by the overlap of a 2D light sheet (2D ODT) and a vertical optical tweezer (OT) with elliptical beamshape. b The resulting level scheme of the non-interacting system is characterized by two quantum numbers (nx, ny). Shown is a closed shell configuration of 5+5 atoms. The Fermi energy is the energy of the highest occupied level. c By lowering the trap depth, the particles leave the trap shell by shell. Counting the number of atoms as a function of the optical trap depth reveals the level structure of the system. For the weakly-interacting system we find, corresponding to B, filled shells of 1+1, 2+2, 3+3, 5+5 and 7+7 atoms.
Extended Data Fig. 2 Momentum space density of 5+5 non-interacting atoms.
Comparison of the experimental and theoretical (a and b, respectively) momentum space density of 5+5 non-interacting atoms in our elliptical trap. The pixel size is given by the pixel size of our camera.
Extended Data Fig. 3 Integrated momentum space density of 5+5 non-interacting atoms.
The measured and the calculated momentum density gets integrated along y- and x- direction (a and b, respectively). In the errors, the theoretical curve coincides with the experimental curves, showing that the non-interacting system is in the ground state of the harmonic oscillator potential.
Extended Data Fig. 4 Ballistic expansion.
Root mean square of the atom positions δrx,y as a function of tint. The dashed lines show the expected ballistic expansion, the solid lines mark the ideal hydrodynamic evolution of the corresponding many-body system.
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Brandstetter, S., Lunt, P., Heintze, C. et al. Emergent interaction-driven elliptic flow of few fermionic atoms. Nat. Phys. 21, 52–56 (2025). https://doi.org/10.1038/s41567-024-02705-8
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DOI: https://doi.org/10.1038/s41567-024-02705-8
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