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arXiv:2508.15626 · Physical Review A

Direct energy dissipation measurements for a driven superfluid via the harmonic-potential theorem

Clara Tanghe, Senne Van Wellen, Kobe Vergaerde, Karel Van Acoleyen

Published Mar 11, 2026• 1 citation
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Abstract

We propose and experimentally demonstrate a method to directly measure energy dissipation for a linearly driven superfluid confined in a harmonic trap. The method relies on a perturbed version of the harmonic-potential theorem, according to which a potential perturbation - effectively acting as a stirrer - converts center-of-mass motional energy into internal energy. Energy conservation then enables a direct, quantitative determination of the dissipated energy from measurements of the macroscopic center-of-mass observables. Applying this method to a perturbed, driven Bose-Einstein condensate, we observe dissipation curves characteristic of superfluid flow, including a critical velocity that depends on the stirrer strength, consistent with previous studies. Our results are supported by mean-field simulations, which corroborate both the theoretical framework and the experimental findings.

DOI
10.1103/v17d-68v7

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We propose and experimentally demonstrate a method to directly measure energy dissipation for a linearly driven superfluid confined in a harmonic trap. The method relies on a perturbed version of the harmonic-potential theorem, according to which a potential perturbation - effectively acting as a stirrer - converts center-of-mass motional energy into internal energy. Energy conservation then enables a direct, quantitative determination of the dissipated energy from measurements of the macroscopic center-of-mass observables. Applying this method to a perturbed, driven Bose-Einstein condensate, we observe dissipation curves characteristic of superfluid flow, including a critical velocity that depends on the stirrer strength, consistent with previous studies. Our results are supported by mean-field simulations, which corroborate both the theoretical framework and the experimental findings.
We create Bose-Einstein condensates of 87Rb in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the Bose-Einstein condensate and accounts for the main features of the observed behavior.
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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 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 vvv. We identify the onset of dissipation by a sharply increasing heating rate above a velocity vc{v}_{c}vc​, which we define as the critical velocity. We show that vc{v}_{c}vc​ 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 vc{v}_{c}vc​ for the parameters similar to the experiments, which is inconsistent with the measurement of nonzero vc{v}_{c}vc​. However, if the heating rate is based on the thermal fraction after a 100ms100\phantom{\rule{4pt}{0ex}}\mathrm{ms}100ms 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.
According to the Landau criterion for superfluidity, a Bose–Einstein condensate flowing with a group velocity smaller than the sound velocity is energetically stable in the presence of perturbing potentials. We found that this is strictly correct only for vanishingly small perturbations. The superfluid critical velocity strongly depends on the strength and shape of the defect. We quantitatively study, both numerically and with an approximate analytical model, the dynamical response of a condensate flowing against an instantaneously raised spatially periodic defect. We found that the critical velocity v c decreases by increasing the strength of the defect V 0 , up to a critical value of the defect intensity where the critical velocity vanishes.