How to Observe Dipolar Effects in Spinor Bose-Einstein Condensates

We propose an experiment which proves the possibility of spinning gaseous media via dipolar interactions in the spirit of the famous Einstein–de Haas effect for ferromagnets. The main idea is to utilize resonances that we find in spinor condensates of alkali atoms while these systems are placed in an oscillating magnetic field. A significant transfer of angular momentum from spin to motional degrees of freedom observed on resonance is a spectacular manifestation of dipolar effects in spinor condensates.

Figure 1

Relative transfer of ${}^{87}\mathrm{Rb}$ atoms to the $m_F=0$ and $m_F=-1$ states as a function of time. The initial number of atoms in the $m_F=+1$ component is $2\times {10}^5$. In the spherically symmetric trap with ${\omega }_{\mathrm{tr}}=2\pi \times 100\mathrm{Hz}$, it corresponds to the maximal density equal to $3\times {10}^{14}{\mathrm{cm}}^{-3}$. The parameters of an oscillating magnetic field are $B_0=-0.92\mathrm{mG}$, $A=0.93\mathrm{mG}$, and $\omega /{\omega }_{\mathrm{tr}}=1/100$. The inset shows transfer of atoms for other resonances: $B_0=-1.43\mathrm{mG}$, $A=1.85\mathrm{mG}$, and $\omega /{\omega }_{\mathrm{tr}}=1/30$.

Figure 2

Maximal (within 2.5 s) transfer of ${}^{23}\mathrm{Na}$ atoms to the $m_F=0$ state as a function of the static magnetic field $|B_0|$. The initial number of atoms in the $m_F=+1$ component is ${10}^8$. In the spherically symmetric trap with ${\omega }_{\mathrm{tr}}=2\pi \times 100\mathrm{Hz}$, it corresponds to the maximal density equal to $1.08\times {10}^{15}{\mathrm{cm}}^{-3}$. The frequency and amplitude of an oscillating magnetic field are $\omega /{\omega }_{\mathrm{tr}}=1/100$ and $A=3.5\mathrm{mG}$, respectively. The inset shows transfer for $B_0=-3.4\mathrm{mG}$.

Figure 3

Nonoscillating part of the magnetic field and “magnetic fieldlike” interactions [as in (7)] along a line parallel to the $z$ axis and radially shifted by $10.5\mu \mathrm{m}$. The static magnetic field at the center of the trap equals $B_0=-14.0\mathrm{mG}$, and its gradient is $2.8\mathrm{mG}/\mathrm{cm}$. Other parameters are $\omega /{\omega }_{\mathrm{tr}}=1/3$ and $A=14.3\mathrm{mG}$. Successive curves (from bottom to top) correspond to times 0.2, 0.4, and 0.8 s as marked by bullets in the inset.