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

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.

Figures (12)

• Figure 1: Time-of-flight resonant absorption images of both the unperturbed (first row) and perturbed (second row) BEC for different drive times ($t_{hold}=0$, see main text). The center of mass position of the unperturbed (perturbed) cloud is indicated by a cross (dot).
• Figure 2: Center of mass motion and internal energy evolution. First two panels: the COM positions $y$ and COM velocities $v$ for the drive of Eq. (\ref{['driveex']}). Third panel: the inferred internal energy evolution, via Eq. (\ref{['intenergyexp']}). Red data-points show our experimental results for the unperturbed case ($\delta V=0$), the red lines show the corresponding theoretical prediction of undamped harmonic motion, Eq. (\ref{['eomunpert']}). Blue data-points show our experimental results for a perturbed case, $\delta V=0.27\mu_0$. The blue lines show the results from our corresponding mean-field simulations (see \ref{['sec:mean-field']}).
• Figure 3: Energy curves. For $\delta V_0=0.27 \mu_0$, the evolution of the total energy $\Delta e$ (black), the COM energy $\Delta e_{COM}$ (yellow) and the internal energy $\Delta e_{int}=\Delta e-\Delta e_{COM}$ (blue), inferred from the COM positions and velocities (see Eq. (\ref{['intenergyexp']})). The data-points show our experimental results, the lines show the results from our mean-field simulations (see \ref{['sec:mean-field']}). Red triangle (cross): estimate of the onset time $t_{onset}$ of dissipation based on the local Landau criterion, from Eq. (\ref{['vcrit']}) (from our mean-field simulations).
• Figure 4: Energy curves for different stirrer strengths. As in \ref{['fig:Energies']}, but now for different stirrer strenghts $\delta V_0/\mu_0=0.04,0.07,0.36,0.55$. Notice the different vertical scale for each stirrer strength $\delta V_0$.
• Figure 5: Mean field simulation. 3D GPE simulation for the potential perturbation $\delta V_0 =0.27 \mu_0$. The upper panel displays the internal energy evolution, with the red cross indicating our mean-field estimate - via the local Landau criterion - of the onset time of dissipation. The middle panel shows column densities $n(x,y)$ at selected times, indicated by black dots in the upper panel. The white dots (crosses) indicate the COM position for the perturbed (unperturbed $\delta V_0=0$) cloud. The lower panel compares the cross-section along the central vertical cut of the simulated column density (orange) with the instantaneous groundstate column density (purple) in the COM rest frame.