Critical Vortex Shedding in a Strongly Interacting Fermionic Superfluid

Jee Woo Park, Bumsuk Ko, and Y. Shin

Phys. Rev. Lett. 121, 225301 – Published 28 November 2018

Abstract

We study the critical vortex shedding in a strongly interacting fermionic superfluid of ${}^{6}{Li}$ across the BEC-BCS crossover. By moving an optical obstacle in the sample and directly imaging the vortices after the time of flight, the critical velocity $u_{vor}$ for vortex shedding is measured as a function of the obstacle travel distance $L$ . The observed $u_{vor}$ increases with decreasing $L$ , where the rate of increase is the highest in the unitary regime. In the deep Bose-Einstein condensation regime, an empirical dissipation model well captures the dependence of $u_{vor}$ on $L$ , characterized by a constant value of $η = - [d (1 / u_{vor}) / d (1 / L)]$ . However, as the system is tuned across the resonance, a step increase of $η$ develops about a characteristic distance $L_{c}$ as $L$ is increased, where $L_{c}$ is comparable to the obstacle size. This bimodal behavior is strengthened as the system is tuned towards the BCS regime. We attribute this evolution of $u_{vor}$ to the emergence of the underlying fermionic degree of freedom in the vortex-shedding dynamics of a Fermi condensate.

Received 22 May 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.225301

Physics Subject Headings (PhySH)

Fermionic condensates Superfluidity

Fermi gases Vortices in superfluids

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Jee Woo Park¹, Bumsuk Ko^1,2, and Y. Shin^1,2,*

¹Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
²Center for Correlated Electron Systems, Institute for Basic Science, Seoul 08826, Korea

^*yishin@snu.ac.kr

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Vol. 121, Iss. 22 — 30 November 2018

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Images

Figure 1
Vortex shedding in a strongly interacting fermionic superfluid. (a) Schematic of the experiment. A cylindrical impenetrable obstacle, consisting of a focused repulsive Gaussian laser beam, is translated at a constant velocity through the center of a disk-shaped strongly interacting fermionic condensate of ${}^{6}{Li}$ . (b) An in situ image of the condensate at unitarity penetrated by the obstacle. (c) The number of vortices (gray squares) and the probability of observing vortex dipoles (blue circles) after sweeping the obstacle as a function of $u$ . The shown data set is obtained at unitarity with $L = 27.7 μ m$ using the quick obstacle switch-off procedure [26]. Each data point comprises at least nine realizations of the same experiment. The black solid line is a sigmoidal fit to the probability. From the fit, $u_{vor}$ is extracted by setting $P (u_{vor}) = 1 / 2$ .
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Figure 2
The measured critical velocity for vortex shedding $u_{vor}$ (filled markers) at different sweeping lengths $L$ and the speed of sound $v_{s, \exp}$ (open diamonds) in the BEC-BCS crossover, in units of the Fermi velocity $v_{F}$ . The error bars for $u_{vor}$ and $v_{s, \exp}$ represent one standard deviation of the sigmoidal fit to $P (u)$ and the linear fit to the density wave propagation, respectively. The unseen error bars are hidden by the markers. The gray dot-dashed line is the theoretical speed of sound $v_{s, theo}$ from quantum Monte Carlo calculations, for column-averaged densities [31]. The black dotted curve is the pair-breaking velocity $v_{pb}$ from the mean-field BCS theory.
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Figure 3
Inverse critical velocity $1 / u_{vor}$ as a function of the inverse sweeping distance $1 / L$ . $u_{vor}$ and $L$ are normalized by the speed of sound $v_{s, theo}$ and the effective obstacle diameter $D$ , respectively. Four representative graphs whose $- 1 / k_{F} a$ is equal to (a) $- 1.9$ , (b) $- 0.88$ , (c) 0, and (d) 0.73 are shown. The solid line is the fit of the dissipation model to the data points with $u_{vor} < v_{s, theo}$ (gray) while excluding those with $u_{vor} > v_{s, theo}$ (red). The dotted line indicates the characteristic $D / L_{c}$ where the bimodality develops. The dot-dashed line marks where $u_{vor} = v_{s, theo}$ . The error bars are one standard deviation of the fit. The insets show the values of $u_{vor}$ as a function of $1 / L$ .
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Figure 4
Characterization of the evolution of $u_{vor} (L)$ in the BEC-BCS crossover. (a) The sweeping distance $L_{c}$ at which a step jump of $\tilde{η}$ , the magnitude of the slope of the fit, is observed (blue triangles), and the value of $L$ where $u_{vor} = v_{s, theo}$ (inverted red triangles). The dashed lines are guides to the eye. (b) $\tilde{η}$ for $L > L_{c}$ (blue circles) and $L < L_{c}$ (gray squares). The blue and gray dashed lines are a guide to the eye. (c) The inverse of the $y$ intercept of the fit, equal to the critical velocity for drag normalized by the speed of sound, for $L > L_{c}$ (blue circles) and $L < L_{c}$ (gray squares). The speed of sound (dot-dashed line) and the pair-breaking velocity (dotted line) normalized by the speed of sound with a multiplicative factor are shown together. The error bars are one standard deviation of the fit.
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