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The paper reports a direct observation of a particular kind of quantum turbulence, called Vinen or “ultraquantum” turbulence, in a homogeneous three-dimensional atomic Bose gas. In this regime the fluid contains a random tangle of vortex lines — thin, line-like defects where the quantum fluid circulates — and the total length of those lines per unit volume, L, is predicted to decay as dL/dt = −B L^2. The authors measure this decay and find quantitative agreement with the Vinen prediction.
To make the vortices visible the team starts from a far-from-equilibrium atomic gas of potassium-39 (39K) held in a cylindrical optical box trap of volume ≈9×10^4 µm^3 and density n ≈ 2.2 µm^−3 (critical temperature ≈70 nK). They prepare an incoherent, low-energy initial state and then turn on interactions at time t = 0 using a Feshbach resonance (magnetic field control of the s-wave scattering length a). To image the vortices they briefly switch off the trap and interactions, use a pulsed harmonic potential as a matter-wave lens to magnify the cloud by about 3.5× in the imaging plane, and then take a picture of a thin central slice of the magnified cloud (slice thickness ≈15 µm).
Vortex lines that cross the imaged slice appear as dark linear dips in the two-dimensional density picture. The in-situ core size set by the healing length is ξ ≈ 1 µm and the theoretical full width at half maximum of the density dip is ≈3 ξ, but the apparent vortex diameter in the images is ≈15 µm because of the magnification, finite imaging resolution (≈5 µm), and some blurring during the short free expansion. To extract the vortex line-length density L the authors count distinct vortex imprints in the slice and use a geometrical relation L = 4 Ni / S, where Ni is the number of intersections of vortex lines with the imaged surface area S.
The main quantitative result is that L(t) follows the Vinen decay law once well-defined vortices have formed (they appear clearly for times t ≳ 80 ms). Fitting the measured L(t) to a model that adds a one-body loss term gives B = 1.0(2) ℏ/m and a one-body time constant τ ≈ 300(40) ms; numerically differentiating the data gives a consistent B = 0.9(2) ℏ/m. The one-body term explains a slower, exponential decay at very long times that is consistent with individual vortices annihilating at the trap walls. The measured prefactor B does not depend noticeably on the (weak) interaction strength a in these experiments.
Why this matters: Vinen turbulence had been well studied in strongly interacting superfluid helium but was harder to pin down in weakly interacting, compressible atomic gases. The result shows that, despite being compressible on small scales, the large-scale decay of the vortex tangle in this atomic gas behaves like an incompressible superfluid and matches the classic Vinen prediction. Important caveats include the limited imaging resolution and the need to image only a thin slice to see individual vortex imprints (whole-cloud images do not show these lines). The measured B has experimental uncertainty (error bars quoted above), and at very long times vortex loss to the trap walls complicates the simple L^2 decay. The PDF excerpt may not contain the full paper, so other experimental details or additional uncertainties could be discussed in the full text.