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arXiv:cond-mat/9907308 · Physical Review A

Bose-Einstein condensation with magnetic dipole-dipole forces

Krzysztof Góral, Kazimierz Rza̧żewski, Tilman Pfau

Published Mar 24, 2000• 350 citations
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Abstract

Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of, e.g., chromium $(6{\ensuremath{\mu}}_{B}),$ and a typical value of the scattering length, all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region, the ground-state wave functions show internal structures that we believe have not been seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.

DOI
10.1103/physreva.61.051601

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Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of, e.g., chromium (6\ensuremathμB),(6{\ensuremath{\mu}}_{B}),(6\ensuremathμB​), and a typical value of the scattering length, all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region, the ground-state wave functions show internal structures that we believe have not been seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.
The ground-state solutions of a dilute Bose condensate with contact and magnetic dipole-dipole interactions are examined. By lowering the value of the scattering length, Goral et al. [Phys. Rev. A 61, 051601 (2000)] numerically predict a region of unstable solutions, accompanied by a neighborhood where the ground-state wave functions have internal structure. On the contrary, we find that the dipolar condensate has an intuitively located stability region, and ground-state solutions near the instability threshold that are without any unusual structure.
We report on the generation of a Bose-Einstein condensate in a gas of chromium atoms, which have an exceptionally large magnetic dipole moment and therefore underlie anisotropic long-range interactions. The preparation of the chromium condensate requires novel cooling strategies that are adapted to its special electronic and magnetic properties. The final step to reach quantum degeneracy is forced evaporative cooling of 52Cr atoms within a crossed optical dipole trap. At a critical temperature of T(c) approximately 700 nK, we observe Bose-Einstein condensation by the appearance of a two-component velocity distribution. We are able to produce almost pure condensates with more than 50,000 condensed 52Cr atoms.
We have observed Bose-Einstein condensation of chromium atoms [1], whose large magnetic dipole moment is unique among all species that have been Bose-condensed so far. The arising magnetic forces are of anisotropic and long-range character and therefore introduce a novel type of interaction in the physics of ultracold quantum gases. In addition, it is expected that the character of the interaction present in a chromium BEC can be varied from mainly contact to purely dipolar utilizing one of the recently observed Feshbach resonances in 52Cr-collisions.
We have measured the relative strength ${\ensuremath{\epsilon}}_{dd}$ of the magnetic dipole-dipole interaction compared with the contact interaction in a dipolar chromium Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of the condensate with different orientations of the atomic magnetic moments. By comparing the experimental results with numerical solutions of the hydrodynamic equations for dipolar condensates, we obtain ${\ensuremath{\epsilon}}_{dd}=0.159\ifmmode\pm\else\textpm\fi{}0.034$. We use this result to determine the sss-wave scattering length $a=(5.08\ifmmode\pm\else\textpm\fi{}1.06\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9})\text{ }\mathrm{m}=(96\ifmmode\pm\else\textpm\fi{}20)\text{ }{a}_{0}$ of 52Cr^{52}\mathrm{Cr}52Cr. This is fully consistent with our previous measurements on the basis of Feshbach resonances and therefore confirms the validity of the theoretical approach used to describe the dipolar Bose-Einstein condensate.
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.
We report on experiments exploring the physics of dipolar quantum gases using a Chromium Bose-Einstein condensate (BEC). By means of a Feshbach resonance, it is possible to reduce the effects of short range interactions and reach a regime where the physics is governed by the long-range, anisotropic dipole-dipole interaction between the large (6μB6 μ_{\rm B}6μB​) magnetic moments of Chromium atoms. Several dramatic effects of the dipolar interaction are observed: the usual inversion of ellipticity of the condensate during time-of flight is inhibited, the stability of the dipolar gas depends strongly on the trap geometry, and the explosion following the collapse of an unstable dipolar condensate displays d-wave like features.