Selected for a Viewpoint in Physics week ending PRL 117, 245301 (2016) PHYSICAL REVIEW LETTERS 9 DECEMBER 2016 Observation of von Kármán Vortex Street in an Atomic Superfluid Gas Woo Jin Kwon,1 Joon Hyun Kim,1,2 Sang Won Seo,2 and Y. Shin1,2,* 1Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea 2Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea (Received 7 August 2016; published 7 December 2016) We report on the experimental observation of vortex cluster shedding from a moving obstacle in an oblate atomic Bose-Einstein condensate. At low obstacle velocities v above a critical value, vortex clusters consisting of two like-sign vortices are generated to form a regular configuration like a von Kármán street, and as v is increased, the shedding pattern becomes irregular with many different kinds of vortex clusters. In particular, we observe that the Stouhal number associated with the shedding frequency exhibits saturation behavior with increasing v. The regular-to-turbulent transition of the vortex cluster shedding reveals remarkable similarities between a superfluid and a classical viscous fluid. Our work opens a new direction for experimental investigations of the superfluid Reynolds number characterizing universal superfluid hydrodynamics. DOI: 10.1103/PhysRevLett.117.245301 The wake behind a moving obstacle is a classic subject circulation are periodically nucleated from the obstacle considered in fluid dynamics. Various flow regimes are [Fig. 1(c)] and for high v, a transition to turbulence classified by the dimensionless Reynolds number develops with irregular emission of many different kinds Re ¼ vD=ν, where v is the obstacle velocity, D is the of large vortex clusters [Fig. 1(d)]. It was noted that regular lateral dimension of the obstacle, and ν is the fluid viscosity vortex shedding is stable only with clusters consisting of [1].AtlowRe< 50, a laminar or steady flow is formed, two like-sign vortices [14–16], and this is referred to as the and as Re is increased, periodic shedding of vortices with quantum version of the von Kármán vortex street in a et al. alternating circulation occurs, which is known as a von superfluid. Furthermore, Reeves [16] observed for Kármán vortex street. The vortex shedding frequency f large Gaussian obstacles that St exhibits a universal relation gives the Stouhal number St ¼ fD=v, which is a dimen- to a superfluid Reynolds number defined as ≡ ðv − v ÞD=ðℏ=mÞ ℏ sionless quantity that is a universal function of Re. With Res c , where is the Planck constant 2π m further increasing Re > 105, the wake dynamics becomes divided by and is the particle mass, and a sudden onset of turbulence at Res ≈ 0.7. The proposed Res was unstable and turbulent flow develops. The transition from applied in the data analysis of turbulence experiments with laminar to turbulent flow represents a universal character- superfluid helium [17]. istic of classical fluid dynamics. An interesting situation arises when a fluid has zero (b) viscosity; i.e., it becomes a superfluid. The Reynolds (a) Optical v number cannot be defined and furthermore, in contrast obstacle to classical fluids, the superfluid carries vorticity in the v<vc form of phase defects with quantized circulation. Would the v (c) superfluid show universal behavior in the wake response to a moving obstacle, and can we define a proper Reynolds BEC – v>vc number Res characterizing it [2 5]? It has been clearly (d) demonstrated that a superfluid becomes dissipative via quantum vortex emission when the obstacle velocity v >> vc exceeds a critical velocity vc [6–13]. Since turbulent flow would be generated by strong perturbations of the obstacle at significantly high v, the key issue is whether regular FIG. 1. (a) Schematic of the experiment. An impenetrable vortex shedding like the von Kármán street occurs in an obstacle, formed by focusing a repulsive Gaussian laser beam, moves at velocity v in a highly oblate Bose-Einstein condensate intermediate v regime. (BEC). Evolution of vortex shedding: (b) no excitations for Recent numerical studies of two-dimensional vortex v<vc, (c) von Kármán street of clusters of two like-sign shedding dynamics in atomic Bose-Einstein condensates quantum vortices for small v>vc [14–16], and (d) turbulent (BECs) presented affirmative answers to the question shedding of diversely clustered vortices for v ≫ vc. Red and blue [14–16]. In a narrow range of v above vc, vortex-antivortex circles represent vortices with clockwise and counterclockwise pairs or clusters of two like-sign vortices with alternating circulations, respectively. 0031-9007=16=117(24)=245301(5) 245301-1 © 2016 American Physical Society PHYSICAL REVIEW LETTERS week ending PRL 117, 245301 (2016) 9 DECEMBER 2016 pffiffiffiffiffiffiffiffiffi In this Letter, we present an experimental study of is cs ¼ μ=m ≈ 5.1 mm=s. The condensate fraction of the quantum vortex shedding from a moving Gaussian obstacle sample is over 80%. in a highly oblate BEC. By means of spatially large BEC An optical obstacle is formed by focusing a repulsive samples and long-distance obstacle motion control, we Gaussian laser beam to the condensate [Fig. 1(a)]. The 1=e2 examine the evolution of the vortex shedding pattern as a waist of the laser beam is σ ¼ 10.3ð11Þ μm ≈ 27ξ and its function of the obstacle velocity v. We observe regular potentialpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi height is V0=μ ≈ 1.8, giving the obstacle diameter shedding of vortex clusters each consisting of two like-sign D ¼ σ 2 lnðV0=μÞ ≈ 29ξ. The obstacle position is con- vortices and a turbulence transition via diversifying the trolled by steering the laser beam with a piezo-driven cluster types. Furthermore, we observe the saturation of the mirror. Initially, we place the obstacle at 62 μm left from Stouhal number with increasing v, which is qualitatively the condensate center, and translate it linearly across the consistent with the numerical results in Ref. [16].Our center region by a distance L ¼ 114 μm at a constant speed results demonstrate remarkable similarities between a v [Fig. 1(a)]. After the obstacle sweeping, we turn off the superfluid and a classical viscous fluid in the wake laser beam linearly within 20 ms, and take an absorption response to a moving obstacle. image of the condensate after 36 ms time of flight [18]. Our vortex shedding experiment is performed with the With this experimental protocol, the critical velocity for apparatus described in Refs. [11–13]. We prepare a highly vortex shedding was measured to be vc ¼ 1.11ð5Þ mm=s. oblate BEC of 23Na atoms in a harmonic trapping potential Note that the local condensate density varies by ≈ 35% which is generated by combining a pancake-shaped optical along the obstacle trajectory. At the initial and final dipole trap and a magnetic quadruple trap. The radial and positions, the local speed of sound and the obstacle axial trapping frequencies are ωr;z ¼ 2π × ð11.1; 400Þ Hz. diameter are 20% smaller and 30% larger than those at 6 The atom number of the condensate is N0 ¼ 5.6ð4Þ × 10 the center, respectively. and thepffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi radial Thomas-Fermi radius of the condensate is Figure 2(a) displays images of condensates for various 2 R ¼ 2μ=mωr ≈ 105 μm, where μ is the condensate obstacle velocities v>vc [Fig. 2(a)]. In the imaging, a chemical potential.pffiffiffiffiffiffiffiffiffi At peak atomic density, the healing vortex cluster appears as a large density-depleted hole length is ξ ¼ ℏ= 2mμ ≈ 0.38 μm and the speed of sound because during the time of flight vortex cores expand and (a) v=1.14 mm/s (b) 0.4 κ=1 23 45 0.2 100 μm v=1.14 mm/s 0.0 1.27 mm/s 0.2 0.1 1.27 mm/s 0.0 1.39 mm/s 0.2 0.1 1.39 mm/s 0.0 0.2 1.43 mm/s 0.1 1.43 mm/s 0.0 0.2 1.50 mm/s 0.1 1.50 mm/s Normalized counts of clusters Increasing obstacle velocity 0.0 0.2 1.68 mm/s 0.1 1.68 mm/s 0.0 0.2 1.97 mm/s 0.1 1.97 mm/s 0.0 50 100 150 200 250 300 Hole area (arb. unit) FIG. 2. Quantum vortex shedding from a moving optical obstacle in a highly oblate BEC. (a) Images of BECs for various obstacle velocities v, taken after 36 ms time of flight [18]. Because of vortex core expansion, a vortex cluster appears with a large density- depleted hole, whose area depends on the cluster charge κ, i.e., the number of vortices in the cluster. (b) Normalized histograms of the cluster hole area. Each histogram was obtained from over 100 image data as in (a). The dashed lines indicate the transition positions for the charge number κ, which are determined from the multiple peak structure of the histograms. 245301-2 PHYSICAL REVIEW LETTERS week ending PRL 117, 245301 (2016) 9 DECEMBER 2016 would merge when they are closely located [18]. Thus, the the quantized charge number κ for vortex clusters. The peak cluster charge κ, i.e., the vortex number of a cluster, can be structure becomes smooth for v>1.6 mm=s because the inferred from the hole area. If some of vortices in a cluster vortex cluster structure is diversified and complicated by have different circulation, it would be indicated by local emitting more vortices. bending of the hole shape [11,13]. For example, we see that Figure 3 displays various characteristics obtained from some of the big clusters for high velocities v ≥ 1.68 mm=s the cluster charge distribution.P The total vortex number is show sharp bending tails in Fig.