arXiv:cond-mat/0002079 · Physical Review A

Trapped atomic condensates with anisotropic interactions

S. Yi, Li You

Published Mar 13, 2000• 325 citations

Abstract

We study ground-state properties of trapped atomic condensates with electric-field-induced dipole-dipole interactions. A rigorous method for constructing the pseudopotential in the spirit of ladder approximation is developed for general nonspherical (polarized) particles interacting anisotropically. We discuss interesting features not previously considered for currently available alkali-metal condensates. In addition, to provide a quantitative assessment for controlling atomic interactions with electric fields, our investigation may also shed a different light into the macroscopic coherence properties of the Bose-Einstein condensation (BEC) of dilute interacting atoms.

DOI: 10.1103/physreva.61.041604

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arXiv:cond-mat/0002079 · Physical Review A

Trapped atomic condensates with anisotropic interactions

S. Yi, Li You

Published Mar 13, 2000• 325 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.61.041604

Related papers

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s

-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range

s

-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.

\sim r^{4}

from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities

\ell =0

(fundamental solitons),

\ell =1

, and

\ell =2

. The fundamental solitons and vortices with

\ell =1

exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with

\ell =2

are stable solely in the isotropic model.

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 (

{}^{52}

Cr,

{}^{164}

Dy,

{}^{168}

Er) 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

{}^{7}

Li,

{}^{39}

K, and

{}^{133}

Cs. 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.