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arXiv:cond-mat/0608171 · Physical Review Letters

Comparing Contact and Dipolar Interactions in a Bose-Einstein Condensate

Axel Griesmaier, J. Stühler, Tobias Benedikt Koch, M. Fattori, Tilman Pfau, S. Giovanazzi

Published Dec 21, 2006• 139 citations
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Abstract

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 $s$-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 $^{52}\mathrm{Cr}$. 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.

DOI
10.1103/physrevlett.97.250402

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 7, 2006•0 citations
We have measured the relative strength \ensuremathϵdd{\ensuremath{\epsilon}}_{dd}\ensuremathϵdd​ 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 \ensuremathϵdd=0.159\ifmmode±\else\textpm\fi0.034{\ensuremath{\epsilon}}_{dd}=0.159\ifmmode\pm\else\textpm\fi{}0.034\ensuremathϵdd​=0.159\ifmmode±\else\textpm\fi0.034. We use this result to determine the sss-wave scattering length a=(5.08\ifmmode±\else\textpm\fi1.06\ifmmode×\else\texttimes\fi10\ensuremath−9) m=(96\ifmmode±\else\textpm\fi20) a0a=(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}a=(5.08\ifmmode±\else\textpm\fi1.06\ifmmode×\else\texttimes\fi10\ensuremath−9) m=(96\ifmmode±\else\textpm\fi20) a0​ 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.
Due to its large magnetic moment of 6 muB, atomic chromium is the only Bose-Einstein condensed species so far to show relatively large magnetic dipole-dipole interactions (MDDI) besides the usual s-wave contact interaction. The long-range (1/r3) and anisotropic character of the MDDI gives birth to unique properties for the Cr Bose-Einstein condensate obtained recently in our group. In particular, it leads to an anisotropic deformation of the expanding condensate which depends on the orientation of the atomic dipole moments (Giovanazzi et al., 2006). In these measurements the dominant interaction is the contact one. We used expansion dynamics measurements to quantify the ratio between dipolar and contact interactions to be epsivdd= 0.159 plusmn 0.034 . This in turn provides a new experimental determination of the chromium scattering length: a = (96 plusmn 20) a0with an accuracy which is not limited by errors in the measurement of the atom number.
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.
Abstract. Ultra-cold atomic systems provide a new setting where to investigate the role of longrange interactions. In this paper we will review the basics features of those physical systems, in particular focusing on the case of Chromium atoms. On the experimental side, we report on the observation of dipolar effects in the expansion dynamics of a Chromium Bose-Einstein condensate. By using a Feshbach resonance, the scattering length characterising the contact interaction can be strongly reduced, thus increasing the relative effect of the dipole-dipole interaction. Such experiments make Chromium atoms the strongest candidates at present for the achievement of the strong dipolar regime. On the theoretical side, we investigate the behaviour of ultra-cold dipolar systems in the presence of a periodic potential. We discuss how to realise this situation experimentally and we characterise the system in terms of its quantum phases and metastable states, discussing in detail the differences with respect to the case of zero-range interactions.
We report on experiments with ultracold chromium atoms. Preparing a cloud of 52Cr atoms in a crossed optical dipole trap (CODT) and applying magnetic fields between 4 and 600 G, we observe 14 Feshbach resonances by the occurrence of increased atom loss at distinct magnetic field values. A comparison with theory taking only dipole–dipole coupling into account shows very good agreement between experimental and theoretical resonance positions and allows us to extract the s-wave scattering lengths a 6=112(14) a 0, a 4= 58(6) a 0, a 2=−7(20) a 0 of the involved molecular potentials as well as the dispersion coefficients C 6= 733(70) au and au. The strongest resonance at 589 G has a calculated width of 1.7 G and reveals a three-body loss coefficient below L 3, max∼3×10−36 m6 s−1. Further evaporative cooling within the CODT leads to the formation of a Bose–Einstein condensate (BEC) with up to 100 000 condensed atoms. The magnetic dipole–dipole interaction between the Cr atoms is so strong that, as a first mechanical manifestation of dipole–dipole interaction, we observe a modification of the condensate expansion which depends on the alignment of the atomic magnetic dipoles with respect to the axis of the CODT. This magnetostrictive effect is in very good agreement with the theory of dipolar quantum gases and shows that a Cr-BEC is an excellent model system to study dipole–dipole interactions in degenerate quantum gases.
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.