We calculate the ground states and ground state phase diagrams of Bose-Einstein condensates of spin-3 atoms under the assumption of conserved magnetization. We especially concentrate on the ground states of a
52Cr condensate. In
52Cr the magnetic dipole-dipole interaction enables magnetization changing collisions, but in a strong magnetic field these are suppressed. In the calculation of the phase diagrams we neglect the contribution from the dipole-dipole interaction, but discuss its effects at the end of the paper. We show that the ground state of a
52Cr condensate does not seem to depend on whether or not the dipole-dipole interaction is taken into attention.
The
s-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the
s-wave interaction in many atomic species. This opens the possibilities to study magnetic dipole-dipole interactions (MDDIs) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDIs on the statics and dynamics of atomic BECs with tunable
s-wave interactions for a variety of species, including both nonalkali metals with large magnetic dipole moments (
52Cr,
164Dy,
168Er) and alkali metals (with much smaller magnetic dipole moments). A parameter of magnetic Feshbach resonances, ${\ensuremath{\epsilon}}_{dd,\text{max}}$, is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors, not only for the strongly magnetic dipolar species but also for the alkali-metal BECs of
7Li,
39K, and
133Cs. In addition, we predict several effects which should be experimentally observable. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.
We theoretically show that the spin Hall effect arises in a Bose-Einstein condensate (BEC) of neutral atoms interacting via the magnetic dipole-dipole interactions (MDDIs). Since the MDDI couples the total spin angular momentum and the relative orbital angular momentum of two colliding atoms, it works as a spin-orbit coupling. Thus, when we prepare a BEC in a magnetic sublevel
m=0, thermally and quantum-mechanically excited atoms in the
m=1 and $\ensuremath{-}1$ states feel the Lorentz-like forces in the opposite directions. This is the origin for the emergence of the spin Hall effect. We define the mass-current and spin-current operators from the equations of continuity and calculate the spin Hall conductivity from the off-diagonal current-current correlation function within the Bogoliubov approximation. We find that the correction of the current operators due to the MDDI significantly contributes to the spin Hall conductivity. A possible experimental situation is also discussed.