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arXiv:1509.02168 · Physical Review A

Probing superfluidity of Bose-Einstein condensates via laser stirring

Vijay Pal Singh, Wolf Weimer, Kai Morgener, Jonas Siegl, Klaus Hueck, Niclas Luick, Henning Moritz, Ludwig Mathey

Published Feb 22, 2016• 46 citations
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Abstract

We investigate the superfluid behavior of a Bose-Einstein condensate of $^{6}\mathrm{Li}$ 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 ${v}_{c}$, 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 ${v}_{c}$. A direct comparison to the experimental data shows excellent agreement.

DOI
10.1103/physreva.93.023634

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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.
We propose quantum stirring with a laser beam as a probe of superfluidity in a strongly interacting one-dimensional Bose gas confined to a ring. Within the Luttinger liquid theory framework, we calculate the fraction of stirred particles per period as a function of the stirring velocity, the interaction strength and the coupling between the stirring beam and the bosons. The fraction of stirred particles crosses over at a critical velocity from a constant at low velocities to a characteristic power law at high velocities. The critical velocity depends on the size of the ring and vanishes in the thermodynamic limit. Details of this cross-over depend on the interaction strength and on the coupling between the stirring beam and the bosons. Our results are relevant for ongoing experiments on ring-trapped Bose-Einstein condensates.
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.