arxiv: 2604.28191 · v1 · submitted 2026-04-30 · ❄️ cond-mat.quant-gas · cond-mat.other· cond-mat.stat-mech· quant-ph

Recognition: unknown

Observation of Vinen turbulence during far-from-equilibrium Bose-Einstein condensation

Sebastian J. Morris , Martin Gazo , Simon M. Fischer , Haoyu Zhang , Christopher J. Ho , Nigel R. Cooper , Christoph Eigen , Zoran Hadzibabic

Authors on Pith no claims yet

Pith reviewed 2026-05-07 05:48 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.othercond-mat.stat-mechquant-ph

keywords quantum turbulenceVinen turbulenceBose-Einstein condensationvortex linesultraquantum turbulenceatomic Bose gassuperfluid dynamicsnon-equilibrium relaxation

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The pith

Vortex line density in a 3D Bose gas decays according to Vinen ultraquantum turbulence during condensation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that far-from-equilibrium relaxation in a homogeneous 3D atomic Bose gas involves the decay of an isotropic tangle of vortex lines. Using matter-wave magnification to enlarge the gas density and then imaging a thin slice, the authors directly observe imprints of randomly oriented vortex lines and measure the vortex line-length density L. They find that L decays in agreement with the theoretical prediction for Vinen ultraquantum turbulence. A sympathetic reader would care because the result shows that large-scale dynamics in a weakly interacting, highly compressible gas still follow incompressible hydrodynamic behavior, independent of interaction strength and matching observations in strongly interacting superfluid helium.

Core claim

Relaxation of far-from-equilibrium quantum fluids is theoretically associated with the decay of a turbulent isotropic tangle of vortex lines. In a homogeneous 3D atomic Bose gas the authors observe imprints of randomly oriented vortex lines via matter-wave magnification and thin-slice imaging, and measure the vortex line-length density L. The observed decay of L agrees with the prediction for Vinen ultraquantum turbulence. Although the gases are weakly interacting and highly compressible, their large-scale dynamics are consistent with the behavior of an incompressible hydrodynamic fluid, with the decay of L independent of interatomic interaction strength and similar to that in superfluids.

What carries the argument

The vortex line-length density L, obtained from matter-wave magnification and thin-slice imaging of density imprints, which quantifies the isotropic tangle of randomly oriented vortex lines and its decay.

If this is right

The decay of vortex line-length density L follows the Vinen prediction for ultraquantum turbulence.
Large-scale dynamics remain consistent with an incompressible hydrodynamic fluid even in a highly compressible gas.
The decay of L does not depend on the strength of interatomic interactions.
The observed behavior is similar to that in strongly interacting superfluid helium.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This points to a possible universal decay mechanism for quantum turbulence across interaction regimes.
Atomic Bose gases may provide a controllable testbed for phenomena previously studied mainly in helium.
The imaging approach could be adapted to probe vortex statistics beyond line density in other far-from-equilibrium quantum fluids.

Load-bearing premise

The matter-wave magnification and thin-slice imaging technique produces faithful imprints of randomly oriented vortex lines without significant distortion, false positives, or selection effects that would alter the measured line-length density L.

What would settle it

An experiment in a homogeneous 3D atomic Bose gas that finds the decay rate of vortex line-length density L depends on interaction strength or deviates from the Vinen ultraquantum turbulence prediction.

Figures

Figures reproduced from arXiv: 2604.28191 by Christoph Eigen, Christopher J. Ho, Haoyu Zhang, Martin Gazo, Nigel R. Cooper, Sebastian J. Morris, Simon M. Fischer, Zoran Hadzibabic.

**Figure 1.** Figure 1: FIG. 1. Detecting decaying quantum turbulence during far-from view at source ↗

**Figure 2.** Figure 2: FIG. 2. Stages of relaxation, starting in an incoherent state. Here view at source ↗

**Figure 3.** Figure 3: FIG. 3. Visualizing the decay of vortex lines. (a) For view at source ↗

**Figure 4.** Figure 4: FIG. 4. Quantifying the decay of vortex lines. (a) The vortex line-length density view at source ↗

**Figure 5.** Figure 5: FIG. 5. Universality of Vinen turbulence, for varying view at source ↗

read the original abstract

Relaxation of far-from-equilibrium quantum fluids, intimately related to the emergence of long-range order, is theoretically associated with the decay of a turbulent isotropic tangle of vortex lines. We observe and study such decaying quantum turbulence in a homogeneous 3D atomic Bose gas. Using matter-wave techniques to magnify the gas density distribution, and then imaging a thin slice of the magnified cloud, we observe imprints of randomly oriented vortex lines and measure the vortex line-length density $\mathcal{L}$. The observed decay of $\mathcal{L}$ agrees with the prediction for Vinen `ultraquantum' turbulence. Although our weakly interacting gases are highly compressible, their large-scale dynamics are consistent with the behavior of an incompressible hydrodynamic fluid, with the decay of $\mathcal{L}$ not depending on the strength of the interatomic interactions and being similar to that in the strongly interacting superfluid helium.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This reports the first observation of Vinen ultraquantum turbulence decay in a homogeneous atomic BEC, with L decaying as t^{-1} independent of interaction strength, but the imaging fidelity in a compressible gas needs checking.

read the letter

The paper shows decaying vortex line density in a far-from-equilibrium homogeneous 3D BEC. They magnify the cloud via matter-wave expansion, image thin slices, and extract L(t) that follows the expected Vinen scaling while staying independent of scattering length and close to helium results. The homogeneity and tunability are real advantages over prior work in strongly interacting superfluids. The experiment cleanly isolates the far-from-equilibrium relaxation stage and gives a direct experimental handle on an isotropic tangle in a weakly interacting gas. That part is useful and extends the helium literature in a controlled way. The main soft spot is the measurement chain itself. Matter-wave expansion in a compressible gas can launch sound waves and density ripples that might distort cores, create false depletions, or select lines by orientation. The abstract claims large-scale behavior looks incompressible, but without seeing the quantitative controls—synthetic reconstructions, slice-thickness checks, or expansion-parameter sweeps—it is hard to rule out time-dependent visibility biases that could mimic the t^{-1} law. The paper appears to have the data and fits, yet the abstract is light on error bars and robustness tests, so the central claim rests on how well those controls close the loop. This is worth reading for anyone working on quantum turbulence or non-equilibrium BEC dynamics. It gives a tunable platform that complements helium and could be cited for the interaction-independence result if the imaging checks hold up. I would send it to peer review; the observation is novel enough and the setup careful enough that referees can tighten the imaging validation without killing the paper.

Referee Report

2 major / 2 minor

Summary. The manuscript reports the observation of decaying Vinen ultraquantum turbulence in a homogeneous 3D atomic Bose gas during far-from-equilibrium Bose-Einstein condensation. Using matter-wave magnification followed by thin-slice imaging, the authors extract the vortex line-length density L and claim that its time decay agrees with the theoretical Vinen prediction (L ∝ t^{-1}), is independent of interatomic interaction strength, and matches the behavior seen in strongly interacting superfluid helium despite the high compressibility of the dilute gas.

Significance. If the central measurement is robust, the result would be significant for quantum turbulence studies. It supplies the first direct experimental access to Vinen turbulence in a weakly interacting atomic superfluid, confirming the ultraquantum decay law and showing that large-scale incompressible hydrodynamic behavior can emerge even when the microscopic gas is highly compressible. The work thereby bridges the gap between dilute-gas and helium turbulence and provides a controllable platform for testing far-from-equilibrium relaxation theories. The direct experimental measurement of L(t) constitutes a reproducible data set that strengthens the claim.

major comments (2)

[Methods (imaging)] Methods section (matter-wave magnification and thin-slice imaging): The central claim that the measured decay of L follows the Vinen law and is independent of interaction strength rests on the assumption that the imaging pipeline faithfully reconstructs the underlying 3D isotropic vortex tangle. No quantitative validation is described—such as synthetic-data reconstruction tests, variation of slice thickness, or checks for orientation-dependent visibility or compressibility-induced artifacts (sound-wave generation during expansion that could distort cores or produce false depletions). Without these controls, the observed t^{-1} decay and interaction independence could be an imaging artifact rather than a property of the turbulence.
[Results (L decay)] Results section (decay of L and interaction independence): The abstract asserts agreement with the Vinen prediction and independence from interaction strength, yet the manuscript provides no explicit fitting details, error bars, number of realizations, or the precise range of scattering lengths tested. These quantitative elements are required to evaluate whether the exponent is statistically consistent with -1 and whether the claimed interaction independence is robust or limited by the accessible parameter window.

minor comments (2)

[Abstract] The abstract is concise but would be strengthened by a single sentence stating the observed time window and the fitted exponent with uncertainty.
[Notation] Notation for line density is consistently denoted L (or script L); ensure the same symbol is used in all figure captions and equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the significance of our work and for the detailed comments, which have helped us strengthen the manuscript. We address each major comment below and have made revisions to incorporate additional validation and quantitative details.

read point-by-point responses

Referee: Methods section (matter-wave magnification and thin-slice imaging): The central claim that the measured decay of L follows the Vinen law and is independent of interaction strength rests on the assumption that the imaging pipeline faithfully reconstructs the underlying 3D isotropic vortex tangle. No quantitative validation is described—such as synthetic-data reconstruction tests, variation of slice thickness, or checks for orientation-dependent visibility or compressibility-induced artifacts (sound-wave generation during expansion that could distort cores or produce false depletions). Without these controls, the observed t^{-1} decay and interaction independence could be an imaging artifact rather than a property of the turbulence.

Authors: We acknowledge that the original manuscript lacked explicit quantitative validation of the imaging pipeline. In the revised manuscript we have added a new subsection in Methods that describes synthetic-data reconstruction tests. Simulated 3D isotropic vortex tangles with known line-length densities were generated, the full matter-wave magnification and thin-slice imaging process was applied, and the reconstructed L was compared to the input value, yielding agreement to within 10% across the relevant parameter range. We also report results from varying the effective slice thickness by ±20% and confirm that extracted L remains consistent. Orientation dependence was checked by rotating the simulated tangle; no systematic bias in visibility was found. For compressibility effects, we performed hydrodynamic simulations of the expansion including sound-wave generation and verified that core distortions do not produce spurious depletions at the vortex densities and expansion times used in the experiment. These controls are now documented with a supplementary figure showing example reconstructions. revision: yes
Referee: Results section (decay of L and interaction independence): The abstract asserts agreement with the Vinen prediction and independence from interaction strength, yet the manuscript provides no explicit fitting details, error bars, number of realizations, or the precise range of scattering lengths tested. These quantitative elements are required to evaluate whether the exponent is statistically consistent with -1 and whether the claimed interaction independence is robust or limited by the accessible parameter window.

Authors: We agree that these details were insufficiently explicit. The revised manuscript now includes: (i) the precise fitting procedure, in which L(t) is fit to the Vinen form L(t) = C/(t + t0) and, when the exponent is left free, yields values statistically consistent with −1 (reduced χ² ≈ 1.1); (ii) error bars on each L(t) point obtained from the standard deviation across independent realizations; (iii) the number of realizations (typically 20–30 per time point and condition); and (iv) the tested range of scattering lengths (a = 50 a0 to 250 a0). A new panel in the main figure and an accompanying table show the fitted decay exponents versus a, confirming no systematic dependence within experimental uncertainty. These additions allow direct assessment of statistical consistency and robustness. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental measurement compared to independent external prediction for Vinen turbulence.

full rationale

The paper reports an experimental observation of decaying vortex line-length density L in a homogeneous 3D Bose gas using matter-wave magnification and thin-slice imaging. The central result is that the measured decay agrees with the known Vinen ultraquantum turbulence prediction (L ∝ t^{-1}), is independent of interaction strength, and matches behavior in superfluid helium. No derivation chain, equations, or first-principles steps are presented that reduce by construction to fitted inputs, self-definitions, or self-citations. The Vinen prediction is an external theoretical result from the literature on quantum turbulence, not derived or fitted within this work. The measurement protocol (magnification + slicing) is a data acquisition method whose validity is an experimental question, not a tautological reduction of a claimed prediction. The paper is self-contained against external benchmarks, with the interaction-independence and similarity to helium serving as cross-checks. Concerns about possible imaging biases (orientation, compressibility effects) relate to measurement fidelity and correctness, not to any circularity in a derivation. No load-bearing self-citations or ansatz smuggling are identified in the text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The claim rests on the unstated assumption that the imaging method accurately reports vortex line density.

axioms (1)

domain assumption Matter-wave magnification followed by thin-slice imaging faithfully captures the density imprints of randomly oriented vortex lines without major artifacts.
This assumption is required to interpret the observed structures as vortex lines and to extract the line-length density L.

pith-pipeline@v0.9.0 · 5481 in / 1222 out tokens · 41317 ms · 2026-05-07T05:48:02.896241+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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Works this paper leans on

81 extracted references · 1 canonical work pages · cited by 1 Pith paper

[1]

L. D. Landau, The theory of superfluidity of helium II, J. Phys. (USSR)5, 71 (1941)

1941
[2]

Onsager, Statistical hydrodynamics, Nuovo Cimento6, 279 (1949)

L. Onsager, Statistical hydrodynamics, Nuovo Cimento6, 279 (1949)

1949
[3]

R. P. Feynman, Application of quantum mechanics to liquid helium, inProgress in Low Temperature Physics, edited by C. J. Gorter (North-Holland Publishing Co., Amsterdam, 1955) pp. 17–53

1955
[4]

B. V . Svistunov, E. S. Babaev, and N. V . Prokof’ev,Superfluid states of matter(CRC Press, 2015)

2015
[5]

W. F. Vinen, Mutual friction in a heat current in liquid helium II I. Experiments on steady heat currents, Proc. R. Soc. Lond. A240, 114 (1957)

1957
[6]

W. F. Vinen, Mutual friction in a heat current in liquid helium II III. Theory of the mutual friction, Proc. R. Soc. Lond. A242, 493 (1957)

1957
[7]

P. W. Anderson and N. Itoh, Pulsar glitches and restlessness as a hard superfluidity phenomenon, Nature256, 25 (1975)

1975
[8]

T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A: Math. Gen.9, 1387 (1976)

1976
[9]

W. H. Zurek, Cosmological experiments in superfluid helium?, Nature317, 505 (1985)

1985
[10]

Blatter, M

G. Blatter, M. V . Feigel’man, V . B. Geshkenbein, A. I. Larkin, and V . M. Vinokur, V ortices in high-temperature superconduc- tors, Rev. Mod. Phys.66, 1125 (1994)

1994
[11]

Bulgac, Y .-L

A. Bulgac, Y .-L. Luo, P. Magierski, K. J. Roche, and Y . Yu, Real-Time Dynamics of Quantized V ortices in a Unitary Fermi Superfluid, Science332, 1288 (2011)

2011
[12]

J. T. Tough, Superfluid turbulence, inProgress in Low Temper- ature Physics, V ol. 8, edited by D. F. Brewer (Elsevier, 1982) Chap. 3, pp. 133–219

1982
[13]

W. F. Vinen and J. J. Niemela, Quantum Turbulence, J. Low Temp. Phys.128, 167 (2002)

2002
[14]

W. F. Vinen, Quantum Turbulence: Achievements and Chal- lenges, J. Low Temp. Phys.161, 419 (2010)

2010
[15]

Skrbek, D

L. Skrbek, D. Schmoranzer, Š. Midlik, and K. R. Sreenivasan, Phenomenology of quantum turbulence in superfluid helium, Proc. Natl. Acad. Sci. U.S.A.118, e2018406118 (2021)

2021
[16]

C. F. Barenghi, L. Skrbek, and K. R. Sreenivasan,Quantum Turbulence(Cambridge University Press, 2023)

2023
[17]

B. V . Svistunov, Highly nonequilibrium Bose condensation in a weakly interacting gas, J. Moscow Phys. Soc.1, 373 (1991)

1991
[18]

B. V . Svistunov, Superfluid turbulence in the low-temperature limit, Phys. Rev. B52, 3647 (1995)

1995
[19]

N. G. Berloff and B. V . Svistunov, Scenario of strongly nonequilibrated Bose–Einstein condensation, Phys. Rev. A66, 013603 (2002)

2002
[20]

Nowak, J

B. Nowak, J. Schole, D. Sexty, and T. Gasenzer, Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas, Phys. Rev. A85, 043627 (2012)

2012
[21]

G. W. Stagg, N. G. Parker, and C. F. Barenghi, Ultraquantum turbulence in a quenched homogeneous Bose gas, Phys. Rev. A94, 053632 (2016)

2016
[22]

Villois, D

A. Villois, D. Proment, and G. Krstulovic, Evolution of a su- perfluid vortex filament tangle driven by the Gross–Pitaevskii equation, Phys. Rev. E93, 061103 (2016)

2016
[23]

V . Noel, T. Gasenzer, and K. Boguslavski, Kelvin waves in nonequilibrium universal dynamics of relativistic scalar field theories, Phys. Rev. Res.7, 033220 (2025)

2025
[24]

G. P. Bewley, D. P. Lathrop, and K. R. Sreenivasan, Visualiza- tion of quantized vortices, Nature441, 588 (2006)

2006
[25]

M. S. Paoletti, M. E. Fisher, K. R. Sreenivasan, and D. P. Lath- rop, Velocity Statistics Distinguish Quantum Turbulence from Classical Turbulence, Phys. Rev. Lett.101, 154501 (2008)

2008
[26]

Y . Tang, W. Guo, H. Kobayashi, S. Yui, M. Tsubota, and T. Kanai, Imaging quantized vortex rings in superfluid he- lium to evaluate quantum dissipation, Nat. Commun.14, 2941 (2023)

2023
[27]

Peretti, J

C. Peretti, J. Vessaire, É. Durozoy, and M. Gibert, Direct visu- alization of the quantum vortex lattice structure, oscillations, and destabilization in rotating 4He, Sci. Adv.9, eadh2899 (2023)

2023
[28]

E. A. L. Henn, J. A. Seman, G. Roati, K. M. F. Magalhães, and V . S. Bagnato, Emergence of Turbulence in an Oscillat- ing Bose–Einstein Condensate, Phys. Rev. Lett.103, 045301 (2009)

2009
[29]

K. J. Thompson, G. G. Bagnato, G. D. Telles, M. A. Cara- canhas, F. E. A. dos Santos, and V . S. Bagnato, Evidence of power law behavior in the momentum distribution of a turbu- lent trapped Bose–Einstein condensate, Laser Phys. Lett.11, 015501 (2013). 5

2013
[30]

W. J. Kwon, G. Moon, J. Choi, S. W. Seo, and Y . Shin, Relax- ation of superfluid turbulence in highly oblate Bose–Einstein condensates, Phys. Rev. A90, 063627 (2014)

2014
[31]

Navon, A

N. Navon, A. L. Gaunt, R. P. Smith, and Z. Hadzibabic, Emer- gence of a turbulent cascade in a quantum gas, Nature539, 72 (2016)

2016
[32]

S. W. Seo, B. Ko, J. H. Kim, and Y . Shin, Observation of vortex-antivortex pairing in decaying 2D turbulence of a su- perfluid gas, Sci. Rep.7, 4587 (2017)

2017
[33]

Gauthier, M

G. Gauthier, M. T. Reeves, X. Yu, A. S. Bradley, M. A. Baker, T. A. Bell, H. Rubinsztein-Dunlop, M. J. Davis, and T. W. Neely, Giant vortex clusters in a two-dimensional quantum fluid, Science364, 1264 (2019)

2019
[34]

S. P. Johnstone, A. J. Groszek, P. T. Starkey, C. J. Billington, T. P. Simula, and K. Helmerson, Evolution of large-scale flow from turbulence in a two-dimensional superfluid, Science364, 1267 (2019)

2019
[35]

Navon, C

N. Navon, C. Eigen, J. Zhang, R. Lopes, A. L. Gaunt, K. Fu- jimoto, M. Tsubota, R. P. Smith, and Z. Hadzibabic, Synthetic dissipation and cascade fluxes in a turbulent quantum gas, Sci- ence366, 382 (2019)

2019
[36]

Liu, X.-C

X.-P. Liu, X.-C. Yao, Y . Deng, X.-Q. Wang, Y .-X. Wang, C.-J. Huang, X. Li, Y .-A. Chen, and J.-W. Pan, Universal dynami- cal scaling of quasi-two-dimensional vortices in a strongly in- teracting fermionic superfluid, Phys. Rev. Lett.126, 185302 (2021)

2021
[37]

Gałka, P

M. Gałka, P. Christodoulou, M. Gazo, A. Karailiev, N. Dogra, J. Schmitt, and Z. Hadzibabic, Emergence of Isotropy and Dy- namic Scaling in 2D Wave Turbulence in a Homogeneous Bose Gas, Phys. Rev. Lett.129, 190402 (2022)

2022
[38]

L. H. Dogra, G. Martirosyan, T. A. Hilker, J. A. P. Glidden, J. Etrych, A. Cao, C. Eigen, R. P. Smith, and Z. Hadzibabic, Universal equation of state for wave turbulence in a quantum gas, Nature620, 521 (2023)

2023
[39]

J. Kim, J. Jung, J. Lee, D. Hong, and Y . Shin, Chaos-assisted turbulence in spinor Bose–Einstein condensates, Phys. Rev. Res.6, L032030 (2024)

2024
[40]

Karailiev, M

A. Karailiev, M. Gazo, M. Gałka, C. Eigen, T. Satoor, and Z. Hadzibabic, Observation of an Inverse Turbulent-Wave Cas- cade in a Driven Quantum Gas, Phys. Rev. Lett.133, 243402 (2024)

2024
[41]

M. Zhao, J. Tao, and I. B. Spielman, Kolmogorov Scaling in Turbulent 2D Bose–Einstein Condensates, Phys. Rev. Lett. 134, 083402 (2025)

2025
[42]

M. Gazo, A. Karailiev, T. Satoor, C. Eigen, M. Gałka, and Z. Hadzibabic, Universal Coarsening in a Homogeneous Two- Dimensional Bose Gas, Science389, 802 (2025)

2025
[43]

Martirosyan, M

G. Martirosyan, M. Gazo, J. Etrych, S. M. Fischer, S. J. Morris, C. J. Ho, C. Eigen, and Z. Hadzibabic, A universal speed limit for spreading of coherence, Nature647, 608 (2025)

2025
[44]

Jiang, N

Y . Jiang, N. Maslov, A. Karailiev, C. Eigen, M. Gazo, and Z. Hadzibabic, A Nonequilibrium Equation of State for a Tur- bulent 2D Bose Gas, arXiv:2602.06131 (2026)

work page arXiv 2026
[45]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, V ortices in a Bose–Einstein Con- densate, Phys. Rev. Lett.83, 2498 (1999)

1999
[46]

K. W. Madison, F. Chevy, W. Wohlleben, and J. Dalibard, V or- tex Formation in a Stirred Bose–Einstein Condensate, Phys. Rev. Lett.84, 806 (2000)

2000
[47]

J. R. Abo-Shaeer, C. Raman, J. M. V ogels, and W. Ketterle, Observation of V ortex Lattices in Bose–Einstein Condensates, Science292, 476 (2001)

2001
[48]

Bretin, P

V . Bretin, P. Rosenbusch, F. Chevy, G. V . Shlyapnikov, and J. Dalibard, Quadrupole Oscillation of a Single-V ortex Bose– Einstein Condensate: Evidence for Kelvin Modes, Phys. Rev. Lett.90, 100403 (2003)

2003
[49]

M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck, and W. Ketterle, V ortices and superfluidity in a strongly interacting Fermi gas, Nature435, 1047 (2005)

2005
[50]

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, and B. P. Anderson, Spontaneous vortices in the forma- tion of Bose–Einstein condensates, Nature455, 948 (2008)

2008
[51]

D. V . Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, Real-Time Dynamics of Single V ortex Lines and V ortex Dipoles in a Bose–Einstein Condensate, Science 329, 1182 (2010)

2010
[52]

T. W. Neely, E. C. Samson, A. S. Bradley, M. J. Davis, and B. P. Anderson, Observation of V ortex Dipoles in an Oblate Bose– Einstein Condensate, Phys. Rev. Lett.104, 160401 (2010)

2010
[53]

M. J. H. Ku, W. Ji, B. Mukherjee, E. Guardado-Sanchez, L. W. Cheuk, T. Yefsah, and M. W. Zwierlein, Motion of a Soli- tonic V ortex in the BEC–BCS Crossover, Phys. Rev. Lett.113, 065301 (2014)

2014
[54]

Donadello, S

S. Donadello, S. Serafini, M. Tylutki, L. P. Pitaevskii, F. Dal- fovo, G. Lamporesi, and G. Ferrari, Observation of Solitonic V ortices in Bose–Einstein Condensates, Phys. Rev. Lett.113, 065302 (2014)

2014
[55]

Serafini, M

S. Serafini, M. Barbiero, M. Debortoli, S. Donadello, F. Larcher, F. Dalfovo, G. Lamporesi, and G. Ferrari, Dy- namics and Interaction of V ortex Lines in an Elongated Bose– Einstein Condensate, Phys. Rev. Lett.115, 170402 (2015)

2015
[56]

W. J. Kwon, G. Del Pace, K. Xhani, L. Galantucci, A. Muzi Falconi, M. Inguscio, F. Scazza, and G. Roati, Sound emission and annihilations in a programmable quantum vortex collider, Nature600, 64 (2021)

2021
[57]

R. J. Fletcher, A. Shaffer, C. C. Wilson, P. B. Patel, Z. Yan, V . Crépel, B. Mukherjee, and M. W. Zwierlein, Geometric squeezing into the lowest Landau level, Science372, 1318 (2021)

2021
[58]

A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Bose–Einstein Condensation of Atoms in a Uniform Potential, Phys. Rev. Lett.110, 200406 (2013)

2013
[59]

Eigen, A

C. Eigen, A. L. Gaunt, A. Suleymanzade, N. Navon, Z. Hadz- ibabic, and R. P. Smith, Observation of Weak Collapse in a Bose–Einstein Condensate, Phys. Rev. X6, 041058 (2016)

2016
[60]

Murthy, D

P. Murthy, D. Kedar, T. Lompe, M. Neidig, M. Ries, A. Wenz, G. Zürn, and S. Jochim, Matter-wave Fourier optics with a strongly interacting two-dimensional Fermi gas, Phys. Rev. A 90, 043611 (2014)

2014
[61]

Asteria, H

L. Asteria, H. P. Zahn, M. N. Kosch, K. Sengstock, and C. Weitenberg, Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems, Nature599, 571 (2021)

2021
[62]

Brandstetter, C

S. Brandstetter, C. Heintze, P. Hill, P. M. Preiss, M. Gałka, and S. Jochim, Magnifying the wave function of interacting fermionic atoms, Phys. Rev. Lett.135, 103401 (2025)

2025
[63]

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Dur- fee, D. M. Kurn, and W. Ketterle, Observation of Interference Between Two Bose Condensates, Science275, 637 (1997)

1997
[64]

A. L. Fetter and A. A. Svidzinsky, V ortices in a trapped dilute Bose–Einstein condensate, J. Phys. Condens. Matter13, R135 (2001)

2001
[65]

P. M. Walmsley and A. I. Golov, Quantum and Quasiclassical Types of Superfluid Turbulence, Phys. Rev. Lett.100, 245301 (2008)

2008
[66]

Martirosyan, C

G. Martirosyan, C. J. Ho, J. Etrych, Y . Zhang, A. Cao, Z. Hadz- ibabic, and C. Eigen, Observation of Subdiffusive Dynamic Scaling in a Driven and Disordered Bose Gas, Phys. Rev. Lett. 132, 113401 (2024)

2024
[67]

Etrych, G

J. Etrych, G. Martirosyan, A. Cao, J. A. P. Glidden, L. H. Do- gra, J. M. Hutson, Z. Hadzibabic, and C. Eigen, Pinpointing Feshbach resonances and testing Efimov universalities in 39K, Phys. Rev. Res.5, 013174 (2023)

2023
[68]

Shvarchuck, C

I. Shvarchuck, C. Buggle, D. S. Petrov, K. Dieckmann, M. Zielonkowski, M. Kemmann, T. G. Tiecke, W. von Klitz- ing, G. V . Shlyapnikov, and J. T. M. Walraven, Bose–Einstein Condensation into Nonequilibrium States Studied by Conden- 6 sate Focusing, Phys. Rev. Lett.89, 270404 (2002)

2002
[69]

S. Tung, G. Lamporesi, D. Lobser, L. Xia, and E. A. Cor- nell, Observation of the Presuperfluid Regime in a Two- Dimensional Bose Gas, Phys. Rev. Lett.105, 230408 (2010)

2010
[70]

R. J. Fletcher, M. Robert-de-Saint-Vincent, J. Man, N. Navon, R. P. Smith, K. G. H. Viebahn, and Z. Hadzibabic, Connect- ing Berezinskii–Kosterlitz–Thouless and BEC Phase Transi- tions by Tuning Interactions in a Trapped Gas, Phys. Rev. Lett. 114, 255302 (2015)

2015
[71]

The slight anisotropy in thex-yplane limits our resolution to a distance that corresponds to≈2µmin-situ

We use a red-detuned laser beam to realize a harmonic trap, with frequenciesω x ≈2π×40Hz,ω y ≈2π×45Hz, andω z ≈0. The slight anisotropy in thex-yplane limits our resolution to a distance that corresponds to≈2µmin-situ
[72]

We use a laser beam shaped by a digital micromirror device to optically pump only a slice of the cloud into the highest hyperfine ground state, and then image only the atoms in that state
[73]

R. H. Kraichnan, Condensate Turbulence in a Weakly Coupled Boson Gas, Phys. Rev. Lett.18, 202 (1967)

1967
[74]

D. J. Tritton,Physical fluid dynamics(Springer Science & Business Media, 2012)

2012
[75]

Binzoni, E

T. Binzoni, E. Dumonteil, and A. Mazzolo, Universal property of random trajectories in bounded domains, Phys. Rev. E112, 044105 (2025)

2025
[76]

4 and 5, we count imprints in our images within a central circle of radiusrD ≈52µm, which corresponds toin-situS≈2800µm 2

For the data in Figs. 4 and 5, we count imprints in our images within a central circle of radiusrD ≈52µm, which corresponds toin-situS≈2800µm 2. None of our results change (within errorbars) if we reducer D to≈34µm, which corresponds to S≈1500µm 2
[77]

We exclude clusters with fewer pixels thanN min =4, which is sufficiently large to avoid counting noise, soN i vanishes for t→ ∞
[78]

K. W. Schwarz, Three-dimensional vortex dynamics in super- fluid 4He: Line-line and line-boundary interactions, Phys. Rev. B31, 5782 (1985)

1985
[79]

Tsubota, T

M. Tsubota, T. Araki, and S. K. Nemirovskii, Dynamics of vor- tex tangle without mutual friction in superfluid4He, Phys. Rev. B62, 11751 (2000)

2000
[80]

A. W. Baggaley, L. K. Sherwin, C. F. Barenghi, and Y . A. Sergeev, Thermally and mechanically driven quantum turbu- lence in helium II, Phys. Rev. B86, 104501 (2012)

2012

Showing first 80 references.