Supersonic Rotation of a Superfluid: A Long-Lived Dynamical Ring

We present the experimental realization of a long-lived superfluid flow of a quantum gas rotating in an anharmonic potential, sustained by its own angular momentum. The gas is set into motion by rotating an elliptical deformation of the trap. An evaporation selective in angular momentum yields an acceleration of rotation until the density vanishes at the trap center, resulting in a dynamical ring with $\simeq 350\hslash$ angular momentum per particle. The density profile of the ring corresponds to the one of a quasi two-dimensional superfluid, with a linear velocity reaching Mach 18 and a rotation lasting more than a minute.

Figure 1

(a) Computed density contour (red annulus) for a BEC rotating at $1.06{\omega }_r$ in the shell trap (gray ellipsoid). (b) In situ integrated 2D density (in units of $\mu {\mathrm{m}}^{-2}$) of a dynamical ring rotating at Mach 15, with $2\times {10}^4$ atoms. Image taken 48 s after the end of the stirring procedure. The green dashed ellipsoid is a fit of the ring shape, see text for details.

Figure 2

Sketch of the experimental procedure (see text for detail on the stirring, evaporation, and optional spectroscopy stages) and in situ images of the atomic distribution. The leftmost image shows a cloud at rest before the stirring procedure: only $\sim 10\%$ of the atoms are imaged. As the cloud is set into rotation the peak density decreases and we use two different color scales for pictures taken before and after $t=25\mathrm{s}$, for which the darkest pixels correspond to densities of 50 and $20\mu {\mathrm{m}}^{-2}$, respectively. The three last images correspond to rotations at Mach 11.7, 15.6, and 18.4, respectively.

Figure 3

(a) Time evolution of the effective rotation frequency $\mathrm{\Omega }$ (symbols) compared to the value of ${\mathrm{\Omega }}_h$ (red solid line). Filled blue diamonds: $\mathrm{\Omega }$ extracted from the fit of the density by an ellipse. Dashed blue lines: associated systematic uncertainty induced by the ring anisotropy. Open red circles: same results taking into account the finite optical resolution, see text for details. (b) Radial density profile at $t=35\mathrm{s}$ (open magenta circles) compared to two models: a semiclassical Hartree-Fock model at the critical temperature (solid red line) and a TF model (solid blue line). The two models include a 2D convolution with a Gaussian of $\sigma \simeq 4\mu \mathrm{m}$ to account for the optical resolution. The dashed lines show the predicted density profiles before the convolution.

Figure 4

Cloud anisotropy $\zeta$ as a function of the probe frequency ${\mathrm{\Omega }}_{\mathrm{exc}}$ for different times $t=2.5$, 5, 20, 26, and 50 s from bottom to top, corresponding to effective rotation rates $\mathrm{\Omega }/{\omega }_r\simeq 0.98$, 1.02, 1.03, 1.04, and 1.05 (circle, square, star, diamond, and triangle symbols, respectively). The black solid curves are Lorentzian fits to the data. Inset: example of resonantly excited dynamical ring.