Nonequilibrium Dynamics and Superfluid Ring Excitations in Binary Bose-Einstein Condensates

We revisit a classic study [D. S. Hall et al., Phys. Rev. Lett. 81, 1539 (1998)] of interpenetrating Bose-Einstein condensates in the hyperfine states $|F=1,m_f=-1⟩\equiv |1⟩$ and $|F=2,m_f=+1⟩\equiv |2⟩$ of ${}^{87}\mathrm{Rb}$ and observe striking new nonequilibrium component separation dynamics in the form of oscillating ringlike structures. The process of component separation is not significantly damped, a finding that also contrasts sharply with earlier experimental work, allowing a clean first look at a collective excitation of a binary superfluid. We further demonstrate extraordinary quantitative agreement between theoretical and experimental results using a multicomponent mean-field model with key additional features: the inclusion of atomic losses and the careful characterization of trap potentials (at the level of a fraction of a percent).

Figure 1

Top view of a time sequence of experimental and numerical density profiles for $N=3.50(5)\times {10}^5$ ${}^{87}\mathrm{Rb}$ atoms with equal populations in the $|1⟩$ and $|2⟩$ states. The first row shows the measured density profiles for the $|1⟩$ atoms, while the second and third rows give numerical results including losses and different trap frequencies (Num. A) and without those additional model features (Num. B). A similar arrangement is given for the $|2⟩$ atoms in the fourth, fifth, and sixth rows. The field of view in all pictures is approximately $100\mu \mathrm{m}$ on a side. The evolution time (in ms) for each column is indicated in the top row.

Figure 2

Top panels: 3D renderings of the density distributions in a binary BEC computed from the model at 30 and 80 ms. Each component is depicted by a contour slice at about half of its corresponding maximal density. Red and green surfaces correspond to components $|1⟩$ and $|2⟩$, respectively. The bottom (side) projection corresponds to the $z$- ($x$-) integrated density for the $|1⟩$ component in our model. Bottom panels: radial profiles of the density distributions at 30 and 80 ms. Symbols (squares for $|1⟩$ and circles for $|2⟩$) correspond to the experimental data, which are averaged over the azimuthal angle. Solid lines depict the model results. The middle curve depicts half of the total density, which is nearly preserved during the time evolution [2].

Figure 3

Top panels: experimental and numerical density profiles of a $50:50$ mix of $|1⟩$ and $|2⟩$ atoms at 30 ms for different $N$ as indicated (in thousands of atoms). Different experimental scalings [21] are used to avoid saturating the images. Bottom panels: same as the preceding for different relative numbers of atoms as indicated by the $|1⟩$:$|2⟩$ ratio. The atom number is fixed at $N=3.50(5)\times {10}^5$, as in Fig. 1.