Tuning the dipolar interaction in quantum gases(4)

We have studied the tunability of the interaction between permanent dipoles in Bose-Einstein condensates. Based on time-dependent control of the anisotropy of the dipolar interaction, we show that even the very weak magnetic dipole coupling in alkali gases

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unstable

0o

stable

unstable

l

FIG.3.Stabilityphasediagraminthe -lplane(l=ωz/ωr)obtainedintheThomas-Fermilimit(N→∞)andwithεdd=4.Condensatearealwaysstableinthevicin-ityofthemagicangle M=54.7o.

54.7o90o

istheharmonicpotentialenergyandHint=c2

N2g

2

ingtheexpectationvalueofthetotalenergyHtot=Hho+Hintwhere

22

22

(19)Hho=c1Nm2ωrλr+ωzλz

λrf

1 κ2

3κ2tanh 1

√

3/2

(1 κ2)

(21)

wheredis

theelectricpermanentdipolemomentandaascatteringlength. Theangulardependenceof(9)and(10)3(e(t)· r)2 1foregivenby(11)can berewrittenintermsofspheri-calharmonicsas124π/5Y20.

2

Becauseoftherdependencein(9)onlythe rstquadrupolemodeintheThomas-Fermilimit(withn=0numberofradialnodesinthedensitydisplacementδn)[15]isresonantlyexcited.

S.Stringari,Phys.Rev.Lett.77,2360(1996).

ThequalityfactorQforthequadrupolemodedependsalsoonthetrapgeometry.Q≥2000havebeenob-servedinveryelongatedtrapsbyF.Chevy,etal.,cond-mat/0104218.

M.Mehring,”PrinciplesofHighResolutionNMRinSolids”,(Springer,Berlin,1983).

K.Goral,andL.Santos,cond-mat/0203542;S.YiandL.You,cond-mat/0111256.

Y.CastinandR.Dum,Phys.Rev.Lett.77,5315(1996);V.M.Perez-Garciaetal.,Phys.Rev.Lett.77,5320(1996).

c1andc2dependonlyonn0;becausec1andc2canbereabsorbedinaglobalre-scalingoftheenergyandvaria-tionalparameters,thestudyofthecondensateanisotropyandstabilitydoesnotdependonn0.

12π 0h¯2a

derivesfromanangularintegration.

Thestabilitycanbevariedfora xedvalueofεddandthetrapanisotropyljustvaryingoneeasyexperimentalparameter,namelytheangle .InFig.3weshowoneexampleofhowthestabilityphasediagramforεdd=4canbevariedasfunctionoftheangle .Forverylargeεddthestableregioninthe -lplanebecomesathinregionaroundthemagicangleline.

Conclusion—Wehaveshownthattheanisotropyofthedipole-dipoleinteractionofapolarizedgascanbeusedtotunethestrengthofthedipolarcouplingandtoexcitecollectiveexcitations.Tuningthedipolarcouplingwillbecomeanimportanttoolfordesigningatomicquan-tumgaseswithnovelpropertiesanddynamicalaspects.ThisapproachinopticallytrappedBosecondensedgasesshouldallowtomakeevenveryweakdipolarcouplingvis-iblewithexperimentallyfeasibleparameters(likeB eldsintheGaussregionandspinningfrequenciesuptosev-eral10kHz).Thetuningoftheinteractionmightbecomearelevanttechniqueforstabilizingstronglyinteractingdipolarsystemslikeheteronuclearmoleculargases.

Acknowledgement:—ValuablediscussionwithG.Den-ningerareacknowledged;fundingwasprovidedbytheRTNnetwork”coldquantumgases”underthecon-tractnumberHPRN-CT-2000-00125,andtheDeutscheForschungsgemeinschaft.

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