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Connecting shear flow and vortex array instabilities in annular atomic superfluids


At the interface between two fluid layers in relative motion, infinitesimal fluctuations can be exponentially amplified, inducing vorticity and the breakdown of laminar flow. While shear flow instabilities in classical fluids have been extensively observed in various contexts, controlled experiments in the presence of quantized circulation are quite rare. Here we observe how the contact interface between two counter-rotating atomic superflows develops into an ordered circular array of quantized vortices, which loses stability and rolls up into vortex clusters. We extract the instability growth rates and find that they obey the same scaling relations across different superfluid regimes, ranging from weakly interacting bosonic to strongly correlated fermionic pair condensates. Our results establish connections between vortex arrays and shear flow instabilities, suggesting a possible interpretation of the observed quantized vortex dynamics as a manifestation of the underlying unstable flow. Moreover, they open the way for exploring out-of-equilibrium phenomena such as vortex matter phase transitions and the spontaneous emergence and decay of two-dimensional quantum turbulence.

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Fig. 1: Instability of classical and quantum counter-propagating shear flows.
Fig. 2: Shear flow preparation and emerging vortex dynamics.
Fig. 3: Analysis of the vortex array instability across the BCS–BEC crossover.
Fig. 4: Nonlinear vortex dynamics.

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The data that support the figures within this paper are available from the corresponding author upon reasonable request. Source data are provided with this paper.


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We thank I. Carusotto, N. Cooper and G. Modugno for their valuable comments on the manuscript and the Quantum Gases group at LENS for fruitful discussions. This work was supported by the European Research Council (ERC) under grant agreement no. 307032, the Italian Ministry of University and Research under the PRIN2017 project CEnTraL and PNRR project PE0000023-NQSTI, the European Union’s Horizon 2020 research and innovation programme under the Qombs project FET Flagship on Quantum Technologies grant agreement no. 820419. W.J.K. acknowledges support from the Research Fund (1.220137.01) of UNIST (Ulsan National Institute of Science and Technology). M.M. acknowledges support from grant no. PID2021-126273NB-I00 funded by MCIN/AEI/10.13039/501100011033 and ‘ERDF – A way of making Europe’, and from the Basque Government through grant no. IT1470-22. F.S. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 949438) and from the Italian MUR under the FARE programme (project FastOrbit).

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D.H.-R., G.D.P., F.S., F.M. and G.R. conceived the study. D.H.-R., N.G., G.D.P. and W.J.K. performed the experiments. D.H.-R. and N.G. analysed the experimental data. D.H.-R., K.X., C.F. and M.M. carried out numerical simulations. All authors contributed to the interpretation of the results and to the writing of the manuscript.

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Correspondence to D. Hernández-Rajkov.

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Extended data

Extended Data Fig. 1 Reproducibility of the initial cloud preparation.

a, Fidelity in creating the target circulation state state, 〈ΔwM − ΔwT. b, Number of spurious vortices observed before removing the optical barrier, and c, Deviation of the total number of vortices from the target state, \({\langle {N}_{v}\rangle }_{M}-\Delta {w}_{T}\). All three panels were generated from 100 experimental repetitions for each of the two target states ΔwT = 6, 12 (blue and orange, respectively). d, Total number of vortices detected after removing the barrier, t = 0 of vortex dynamics, as a function of the imprinted winding number difference ΔwT. The red dashed line is the identity line, Nv = Δw.

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Source Data Fig. 3

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Source Data Extended Data Fig. 1

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Hernández-Rajkov, D., Grani, N., Scazza, F. et al. Connecting shear flow and vortex array instabilities in annular atomic superfluids. Nat. Phys. 20, 939–944 (2024).

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