Critical Velocity in the BEC-BCS Crossover

We map out the critical velocity in the crossover from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer superfluidity with ultracold ${}^6\mathrm{Li}$ gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity $v_c$. In the same samples, we measure the speed of sound $v_s$ by exciting density waves and compare the results to the measured values of $v_c$. We perform numerical simulations in the Bose-Einstein condensation regime and find very good agreement, validating the approach. In the strongly correlated regime our measurements of $v_c$ provide a testing ground for theoretical approaches.

Figure 1

A red detuned laser beam with waist $w$ moves through the cloud with velocity $v$, where the obstacle size is on the order of the interparticle separation $d$ (inset). After stirring, the column integrated density ${\tilde{n}}_0(v)$ at the center of the cloud is reduced for $v>v_c$ compared to the unperturbed value, indicating heating. For a superfluid gas (blue circles), the critical velocity $v_c$ can be determined from a bilinear fit (blue line) and in a thermal cloud (red circles and line), no critical velocity can be observed. The data are acquired at $B=806\mathrm{\hspace{0.17em}G}$, $a=13500a_0$ with ${\tilde{n}}_0=1.11\mu {\mathrm{m}}^{-2}$, $N=6100$ for the superfluid.

Figure 2

(a) Critical velocity $v_c$ (green filled circles) and speed of sound $v_s$ (red open circles) in units of the Fermi velocity $v_F$ throughout the BEC-BCS crossover. The error bars correspond to the fit errors. A statistical error for $v_c$ (black open square) was determined from five measurements. The simulated critical velocities are marked with crosses. The solid (dot-dashed) curve is the theory prediction for $v_s$ assuming that the maximum (column averaged) density is relevant for sound propagation, see main text. The dashed line (blue open diamond) represents the pair breaking velocity $v_{\mathrm{pb}}$ as an upper bound for $v_c$ according to BCS mean-field theory (quantum Monte Carlo (QMC) calculations [12]). (b) Dispersion relations for the BEC and the BCS limiting cases (red) and the tangent to this curve from the origin to visualize the Landau criterion (gray).

Figure 3

The simulated heating rates normalized by the stirrer depth $U^2$. The complexity is gradually increased: blue squares depict the idealized case of a very cold homogeneous sample stirred with linear pattern. The relative density excess $\eta$ in the weak stirrer potential $U=k_B\times 2\mathrm{nK}$ is only 3%. For all data sets, the Bogoliubov result for $v_s$ is $4.4\mathrm{mm}/\mathrm{s}$. The red open circles depict a simulation of the experimental case: a trapped sample is stirred circularly with a stirrer of realistic depth. A lower temperature is chosen for technical reasons. Here, the $y$-axis scaling factor is one. In the inset, the results for the heating observed in the central column density ${\tilde{n}}_0(v)$ are compared. We find very good agreement between the experimental (blue filled circles) and the simulated results (red open circles). The bilinear fits to extract $v_c$ are shown with solid lines. In the inset $U=k_B\times 35\mathrm{nK}$.