We study the propagation of electromagnetic waves in the Bose-Einstein condensate of atoms with both intrinsic dipole moments and those induced by the electric field. The modified Gross--Pitaevskii equation is used, which takes into account relaxation and interaction with the electromagnetic field. Two cases are considered: 1) when the dispersion curves of the electromagnetic wave and of the condensate excitations do not intercross and 2) when the condensate excitations' spectrum has a gap and the two dispersion curves do intercross. In the second case the two branches hybridize. It is shown that propagation of sound waves can be accompanied by oscillation of the electromagnetic field. The impact is studied of the dipole-dipole interaction on the character of electromagnetic and acoustic waves' propagation in the Bose-Einstein condensate.
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.
This tutorial presents a detailed discussion of the generation of a Bose–Einstein condensate (BEC) of chromium atoms. This constitutes the first realization of a Bose–Einstein condensate of atoms with strong dipole–dipole interaction. Due to the special electronic and magnetic properties of chromium atoms, standard methods cannot be applied to generate a chromium BEC. The tutorial contains a detailed discussion of the techniques that we use to create the chromium BEC. Compared to all other BECs that have been created so far, chromium atoms have an extraordinarily large magnetic dipole moment and therefore underlie strong magnetic dipole–dipole interaction which is in contrast to the contact interaction that stems from s-wave scattering of the atoms, long-range and anisotropic. A steadily growing number of theoretical publications show that many interesting new phenomena are expected to occur in a 'dipolar' BEC. An experimental investigation of the expansion dynamics of the chromium BEC provides the first experimental proof of a mechanical effect of dipole–dipole interaction in a gas. We describe the condensate by a hydrodynamic model of a superfluid that takes dipole–dipole interaction into account. Our experimental results are in excellent agreement with this theory. We are able to determine the relative strength parameter of the dipole–dipole interaction and deduce the s-wave scattering length of chromium atoms. These two quantities allow us to completely describe the interaction of the atoms in the condensate. The experimental results presented here make the chromium BEC the most promising system for further investigations of dipolar effects in degenerate quantum gases.