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.