Tuning the dipolar interaction in quantum gases

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

Tuningthedipolarinteractioninquantumgases

StefanoGiovanazzi,AxelG¨orlitzandTilmanPfau

5thInstituteofPhysics,UniversityofStuttgart,D-70550Stuttgart,Germany.

(February1,2008)

arXiv:cond-mat/0204352v3 26 Apr 2002

WehavestudiedthetunabilityoftheinteractionbetweenpermanentdipolesinBose-Einsteincondensates.Basedontime-dependentcontroloftheanisotropyofthedipolarin-teraction,weshowthateventheveryweakmagneticdipolecouplinginalkaligasescanbeusedtoexcitecollectivemodes.Furthermore,wediscusshowthee ectivedipolarcouplinginaBose-Einsteincondensatecanbetunedfrompositivetoneg-ativevaluesandevenswitchedo completelybyfastrotationoftheorientationofthedipoles.PACSnumber(s):03.75.Fi,05.30.Jp

IntheBose-Einsteincondensates(BECs)createdthusfar[1]atomsinteractessentiallyonlyatveryshortdis-tance.Atlowtemperatures,theinteractionbetweentheseneutralatomscanbetypicallycharacterizedbyasingleparameter,thes-wavescatteringlength.Themagnitudeandsignofthes-wavescatteringlengthcanbechangedbytuningtheexternalmagnetic eldsinthevicinityofaso-calledFeshbachresonanceThistech-niquehasopenednewpossibilitiesforthestudyandma-nipulationofBECs.Inparticular,thevalueofthes-wavescatteringlengthcanbevariedinrealtime,allowing,forexample,theobservationofcollapsingandexplodingBECs[3].

Inrecentyearsanincreasinginterestisdevotedtodipole-dipoleinteractionsinultracoldgasesDipo-larinteractionswouldlargelyenrichthevarietyofphe-nomenatobeobservedduetotheirlong-rangeandanisotropiccharacter.Ifatomicdipolemomentsaresuf- cientlylarge,theresultingdipole-dipoleforcesmayin- uence,orevencompletelychangethepropertiesofBosegases[4–6,11],theconditionsforBCStransitioninFermigases[7],orthephasediagramforquantumphasetran-sitionsinultracolddipolargasescon nedinopticallat-tices[8].Theinterplayofshort-rangescatteringandlong-rangeinteractionmaygiverisetophenomenalikeferromagneticorderandspinwavesMoreoverthedipolarparticlesareconsideredtobepromisingcandi-datesfortheimplementationoffastandrobustquantum-computingschemesInthisLetter,weconsiderthecaseofpermanent(mag-netic)dipoles.ForalkaliatomswithamagneticmomentmofµB,whereµBisaBohrmagneton,thelongrangepartofthemagneticdipole-dipoleinteractionisgenerallyneglectedsinceitisverysmallcomparedtothes-wavepseudo-potential.Here,weshowthateveninalkaliBECsthisdipolarinteractioncanbemadevisibleifthedipole-dipoleinteractionismodulatedbyrotatingtheatomic

dipoles.Forappropriaterotationfrequencies,acouplingtoelementaryexcitationscanbeachievedleadingtoadynamicgrowthoftheamplitudeoftheexcitation.Inparticular,wewillshowhowthedipolarcouplinginanalkalicondensatecanbeusedtoexcitethequadrupolemodeandhowitispossibletoextractquantitativein-formationabouttheratioofthedipolarcouplingandtheusuals-wavecoupling.

Inensemblesofatomswithalargermagneticmoment,suchaschromiumwherem=6µB,themagneticdipole-dipoleinteractionenergymaybecomecomparableinsizewiththes-wavecontributiontothemean- eldenergy.Therefore,eventhestaticpropertiesofacondensatesuchastheaspectratioaresigni cantlyaltered.Here,weshowhowthee ectivestrengthoftheinteractionandthusitse ectonthestaticpropertiesofacondensatecanbevariedbyfastrotationoftheatomicdipoles.Inthecaseofadipolarinteractionwhichisstrongerthanthes-waveinteractiononlycertaincombinationsoftrapgeometryandorientationofthedipolesleadtoastable(ormetastable)condensate[6,4].Bytuningthedipo-larinteractionunstablecondensatescanthusbetrans-formedintostableonesandviceversa.Inthispaper,westudytheinteractionbetweenpermanentmagneticdipoles.However,themethodsweproposecanalsobeadaptedforparticleswithelectricdipolemomentsuchasheteronuclearmolecules.Inthiscasethedipolarinterac-tionisexpectedtodominateoverthes-waveinteractionandthusthetuningoftheinteractionmightbenecessarytoreachstability.

ManipulatingthemagneticdipolarcouplinginaBEC—Thelong-rangepartoftheinteractionbetweentwomagneticdipolemomentsm1andm2ofatomslo-catedatr1andr2takesthefamiliardependenceUdd(r)=

µ0

r3

(1)

asafunctionoftheinteratomicdistancer=r2 r1,where r=r/randµ0isthemagneticpermeabilityofthevacuum.Weconsiderthecaseofageneraltime-dependenthomogeneousmagnetic eld

B(t)=Be(t),

(2)

slowly-varyingwithrespecttotheLarmorfrequencyωLarmor=mB/¯h,wherem=|m1|=|m2|foridenti-calatoms.Aspin-polarizedatomicensembleswilladia-baticallyfollowtheexternalmagnetic eldB(t)andtheresultinginteratomicenergybecomes

Udd(r,t)=

1

µ0m2

r3

(3)