Observation of Dipole-Induced Spin Texture in an ${}^{87}\mathrm{Rb}$ Bose-Einstein Condensate

We report the formation of spin texture resulting from the magnetic dipole-dipole interaction in a spin-2 ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. The spinor condensate is prepared in the transversely polarized spin state and the time evolution is observed under a magnetic field of 90 mG with a gradient of $3\mathrm{mG}/\mathrm{cm}$ using Stern-Gerlach imaging. The experimental results are compared with numerical simulations of the Gross-Pitaevskii equation, which reveals that the observed spatial modulation of the longitudinal magnetization is due to the spin precession in an effective magnetic field produced by the dipole-dipole interaction. These results show that the dipole-dipole interaction has considerable effects even on spinor condensates of alkali metal atoms.

Figure 1

Schematic illustration of the distributions of the spin vectors $\mathit{f}$ and the effective magnetic field ${\mathit{b}}_{\text{eff}}$ produced by the magnetic dipoles. The ellipsoids on the $z$ axis indicate the shape of the BEC. (a) Initially, $\mathit{f}$ and ${\mathit{b}}_{\text{eff}}$ have the same direction. (b) By an external magnetic field gradient in the $z$ direction, $\mathit{f}$ is twisted and ${\mathit{b}}_{\text{eff}}$ deviates from $\mathit{f}$, which causes precession of $\mathit{f}$ around ${\mathit{b}}_{\text{eff}}$.

Figure 2

(a) Schematic illustration of the experimental setup. The BEC is confined in the crossed FORT and a rf pulse prepares the initial spin state as shown in Fig. 1. After a hold time $T_{\text{hold}}$, the atoms are released from the FORT and the spin components are separated by the SG method. (b) Timing diagram for texture formation and its measurement. The envelope of a $\pi$/2 rf pulse has a Gaussian shape with a standard deviation of 58 $\mu$s.

Figure 3

Absorption images of condensates taken at (a) $T_{\text{hold}}=0\mathrm{ms}$, (b) $T_{\text{hold}}=100\mathrm{ms}$, (c) $T_{\text{hold}}=140\mathrm{ms}$, and (d) $T_{\text{hold}}=400\mathrm{ms}$. In (a), (b), and (c), the magnetic field gradient of $d{B}_z/dz=3\mathrm{mG}/\mathrm{cm}$ is applied along the $z$ direction. In (d), the magnetic field gradient is almost zero.

Figure 4

(a)–(e) Experimentally observed atomic distributions. The absorption images are integrated over $y$. The distances traveled by each component during the SG measurement are subtracted from $z$. (f)–(j) Numerically obtained atomic distributions. The density is integrated over $x$ and $y$. The solid and dashed curves indicate the results with and without the MDDI.

Figure 5

The spatial distributions of spin orientation. (a)–(c) $F_z(z)$ at $T_{\text{hold}}=0\mathrm{ms}$ (dotted curves), 100 ms (dashed curves), and 140 ms (solid curves). (a) is calculated from the experimental results in Figs. 4, 4, and 4. (b) and (c) are the numerical results with and without the MDDI, respectively. (d) and (e) are the numerically obtained spin vectors on the $z$ axis at $T_{\text{hold}}=140\mathrm{ms}$. The color represents the magnitude of $F_z$. The dotted circles mark where the effect of the MDDI is significant.