Controlling phase separation of binary Bose-Einstein condensates via mixed-spin-channel Feshbach resonance

We investigate controlled phase separation of a binary Bose-Einstein condensate in the proximity of a mixed-spin-channel Feshbach resonance in the $|F=1,m_F=+1\rangle$ and $|F=2,m_F=-1\rangle$ states of  ${}^{87}\mathrm{Rb}$ at a magnetic field of 9.10 G. Phase separation occurs on the lower-magnetic-field side of the Feshbach resonance while the two components overlap on the higher-magnetic-field side. The Feshbach resonance curve of the scattering length is obtained from the shape of the atomic cloud by comparison with the numerical analysis of coupled Gross-Pitaevskii equations.

Figure 1

(a) Magnetic-field dependence of the atom number for evolution times $t_{\mathrm{ev}}$ of 25, 50, and 75 ms. (b) Inelastic collision rate estimated by Eq. (2) at $t_{\mathrm{ev}}=25$ ms. Solid lines are Lorentzian functions fit to the data with a center at 9.10 G.

Figure 2

Column densities of the $|2\rangle$ and $|1\rangle$ states obtained by the experiment (upper panels) and the numerical simulation (lower panels) as a function of magnetic field $B_{\mathrm{ev}}$. The field of the view is 316 (vertical) $\times$ 290 $\mu$m (horizontal). The two-body inelastic collision rates $K_{12}$ (${10}^{-13}$ cm${}^3$/s) and the change in the scattering lengths $\Delta a$ used in the numerical simulation are indicated at the bottom.

Figure 3

Numerically obtained column density distributions for various scattering lengths at an evolution time of 75 ms with $K_{12}=3\times {10}^{-13}$ cm${}^3$/s. The relative scattering length $\Delta a$ in units of $a_{\mathrm{B}}$ is indicated in the top row.

Figure 4

Comparison between the experimentally observed density distributions at $B_{\mathrm{ev}}=9.05$ G (dashed lines) and numerical ones (solid lines) obtained for (a) $\Delta a=7.5$$a_{\mathrm{B}}$, (b) $8.0$$a_{\mathrm{B}}$, and (c) $8.5$$a_{\mathrm{B}}$.

Figure 5

Root-mean-square deviation between experiments and calculations at 9.05 G with $K_{12}=3\times {10}^{-13}$ cm${}^3$/s. The dashed line shows $1.3s_{\min }$, which is defined as a threshold for determination of the error bar of the scattering length.

Figure 6

Estimated value of the change in the scattering length between the $|1\rangle$ and $|2\rangle$ states for a magnetic field around the Feshbach resonance. The scattering lengths at $s_{\min }$ are shown as filled squares and fitted by Eq. (3) (solid curve). The open squares correspond to $s$ below the threshold value of $1.3s_{\min }$. The theoretical prediction in Ref. [29] is indicated by the dashed curve.