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arXiv:2110.14634 · Physical Review A

Superfluidity of a laser-stirred Bose-Einstein condensate

Hannes Kiehn, Vijay Pal Singh, Ludwig Mathey

Published Apr 25, 2022• 14 citations
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Abstract

We study superfluidity of a cigar-shaped Bose-Einstein condensate by stirring it with a Gaussian potential oscillating back and forth along the axial dimension of the condensate, motivated by experiments of Raman et al. [Phys. Rev. Lett. 83, 2502 (1999)]. Using classical-field simulations and perturbation theory, we examine the induced heating rate, based on the total energy of the system, as a function of the stirring velocity $v$. We identify the onset of dissipation by a sharply increasing heating rate above a velocity ${v}_{c}$, which we define as the critical velocity. We show that ${v}_{c}$ is influenced by the oscillating motion, the strength of the stirrer, the temperature, and the inhomogeneous density of the cloud. This results in a vanishing ${v}_{c}$ for the parameters similar to the experiments, which is inconsistent with the measurement of nonzero ${v}_{c}$. However, if the heating rate is based on the thermal fraction after a $100\phantom{\rule{4pt}{0ex}}\mathrm{ms}$ equilibration time, our simulation recovers the experimental observations. We demonstrate that this discrepancy is due to the slow relaxation of the stirred cloud and dipole mode excitation of the cloud.

DOI
10.1103/physreva.105.043317

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We investigate the superfluid behavior of a Bose-Einstein condensate of 6Li^{6}\mathrm{Li}6Li molecules. In the experiment by Weimer et al. [Phys. Rev. Lett. 114, 095301 (2015)] a condensate is stirred by a weak, red-detuned laser beam along a circular path around the trap center. The rate of induced heating increases steeply above a velocity vc{v}_{c}vc​, which we define as the critical velocity. Below this velocity, the moving beam creates almost no heating. In this paper, we demonstrate a quantitative understanding of the critical velocity. Using both numerical and analytical methods, we identify the nonzero temperature, the circular motion of the stirrer, and the density profile of the cloud as key factors influencing the magnitude of vc{v}_{c}vc​. A direct comparison to the experimental data shows excellent agreement.
We investigate the superfluid behavior of a two-dimensional (2D) Bose gas of 87Rb^{87}\mathrm{Rb}87Rb atoms using classical field dynamics. In the experiment by R. Desbuquois et al. [Nat. Phys. 8, 645 (2012)], a 2D quasicondensate in a trap is stirred with a blue-detuned laser beam along a circular path around the trap center. Here, we study this experiment from a theoretical perspective. The heating induced by stirring increases rapidly above a velocity vc{v}_{c}vc​, which we define as the critical velocity. We identify the superfluid, the crossover, and the thermal regime by a finite, a sharply decreasing, and a vanishing critical velocity, respectively. We demonstrate that the onset of heating occurs due to the creation of vortex-antivortex pairs. A direct comparison of our numerical results to the experimental ones shows a good agreement, if a systematic shift of the critical phase-space density is included. We relate this shift to the absence of thermal equilibrium between the condensate and the thermal wings, which were used in the experiment to extract the temperature. We expand on this observation by studying the full relaxation dynamics between the condensate and the thermal cloud.
Motivated by a recent experiment [K. C. Wright et al., Phys. Rev. A 88, 063633 (2013)], we investigate the microscopic mechanism for excitation of vortices and formation of a persistent current in an annular BEC stirred by a narrow blue-detuned optical beam. In the framework of a two-dimensional mean-field model, we study the dissipative dynamics of the condensate with parameters that reflect realistic experimental conditions. Vortex-antivortex pairs appear near the center of the stirrer in the bulk of the condensate for slow motion of the stirring beam. When the barrier angular velocity is above some critical value, an outer edge surface mode develops and breaks into the vortices entering the condensate annulus. We determine the conditions for creation of vortex excitations in the stirred toroidal condensate and compare our results with experimental observations.
The ability to support frictionless motion is one of the manifestations of superfluidity. An impurity immersed in a superfluid can move without dissipation below the critical velocity, which, according to the Landau criterion, is determined by the elementary excitation spectrum of the system. In a quantum gas of the ultracold atoms, the critical velocity can be measured by stirring a laser beam through the atomic cloud, and the emergence of dissipation can be observed via the heating effect above the threshold stirring speed. Recently, such a technique is exploited to study the superfluidity of the Bose-Einstein condensate (BEC) of 162Dy atoms with dipole-dipole interactions. It is shown that both the critical velocity and the heating rate reflect the anisotropy of the underlying dipolar excitation spectrum. In this work, we theoretically investigate the anisotropic dissipation of a point-like impurity moving through a dipolar BEC. For the motion along the principal axis, the dissipation rate above the critical velocity is analytically derived according to the linear response theory. At a given reduced velocity, we find the dissipation rate being of a higher value in the direction parallel to the dipole moment, which qualitatively explains the recent experimental observation in dysprosium atoms. Moreover, in the moving direction away from the principal axis, the asymptotic expressions for the dissipation rate are obtained in the high-speed limit, as well as in the regime close to the dissipation threshold. By combining these analytical results with the numerical calculations, we conclude that, in a dipolar BEC, the angular dependence of the dissipation rate always shows the same anisotropy as the critical velocity. Our predictions can be examined in the current experiments with cold atoms, and the results presented here may be also helpful in understanding the anisotropic superfluidity in other systems.
We numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept an obstacle formed by an optical dipole potential through the long axis of the condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of v≈0.3v\approx 0.3v≈0.3 mm/s, suggestive of a superfluid critical velocity substantially less than the average speed of sound. However, our analysis shows that the that the experimental observations of Engels and Atherton are in fact consistent with a superfluid critical velocity equal to the local speed of sound. We construct a model of energy transfer to the system based on the local density approximation to explain the experimental observations, and propose and simulate experiments that sweep potentials through harmonically trapped condensates at a constant fraction of the local speed of sound. We find that this leads to a sudden onset of excitations above a critical fraction, in agreement with the Landau criterion for superfluidity.
We have measured the damped motion of a trapped Bose-Einstein condensate, oscillating with respect to a thermal cloud.The cigar-shaped trapping potential provides enough transverse confinement that the dynamics of the system are intermediate between three-dimensional and onedimensional.We find that the scaling of the damping rate with temperature is consistent with Landau theory, but that the damping rate for axial oscillations at a given temperature is consistently smaller than expected for a three-dimensional gas.We attribute this to the suppressed density of states for low-energy transverse excitations (essential excitations for axial Landau damping), which results from the quantization of the radial motion.