Thermal friction on quantum vortices in a Bose-Einstein condensate

We investigate the dissipative dynamics of a corotating vortex pair in a highly oblate axisymmetric Bose-Einstein condensate trapped in a harmonic potential. The initial vortex state is prepared by creating a doubly charged vortex at the center of the condensate and letting it dissociate into two singly charged vortices. The separation of the vortex pair gradually increases over time and its increasing rate becomes higher with increasing the sample temperature $T$. The evolution of the vortex state is well described with a dissipative point vortex model including longitudinal friction on the vortex motion. For condensates of sodium atoms having a chemical potential of $\mu \approx k_B\times 120$ nK, we find that the dimensionless friction coefficient $\alpha$ increases from 0.01 to 0.03 over the temperature range of $200\text{nK}<T<450$ nK.

Figure 1

Corotating vortex pair in a Bose-Einstein condensate. Images of the condensate at various hold times after creating a doubly charged vortex. The doubly charged vortex splits into two singly charged vortices, and at long times, the vortex pair becomes further separated.

Figure 2

Evolution of the corotating vortex pair in a trapped Bose-Einstein condensate. (a) The vortex state is characterized by two configuration parameters: the separation distance $r_{12}$ of the two vortices and the radial position $r_c$ of the vortex pair center. The radius of the trapped condensate is denoted by $R$. Temporal evolutions of (b) $r_{12}$ and (c) $r_c$ for various sample temperatures. Each data point was obtained by ten measurements of the same experiment, and its error bar indicates the standard deviation of the measurements. The inset in (b) shows the variation of the sample temperature $T$ during the evolution. In the measurements, $R\approx 76\mu \text{m}$ and the chemical potential of the condensate $\mu \approx k_B\times 120$ nK.

Figure 3

Numerical simulation of the dissipative point vortex model. (a)–(c) Trajectories of the two vortices for various initial conditions at $t=1$ s: $r_{12}=10\mu \text{m},\theta =\pi /2$, and $r_c=0\mu \text{m}$ in (a), $7\mu \text{m}$ in (b), and $15\mu \text{m}$ in (c). In the simulation, the friction coefficient $\alpha =0.02,R=76\mu \text{m}$, and ${\mathrm{\Omega }}_0/2\pi =0.64$ Hz. (d), (e) Corresponding evolutions of $r_{12}$ and $r_c$, respectively, for the vortex trajectories in (a)–(c).

Figure 4

Friction coefficient $\alpha$ as a function of $T$. Using Eq. (4), $\alpha$ was determined from the experimental data in Fig. 2 (see the text for details). The solid line is the theoretical prediction of Fedichev et al. [15] and the dashed line is a linear fit to the three lowest-temperature data points. The inset displays $\alpha$ as a function of $T/T_c$. $T_c$ is the critical temperature of the trapped sample. The open circles show the numerical result of Jackson et al. [19], which was obtained for the decay of a single vortex in rubidium gases at fixed $T_c$.