Scattering of two-dimensional solitons in dipolar Bose-Einst

We analyze the scattering of bright solitons in dipolar Bose-Einstein condensates placed in unconnected layers. Whereas for short-range interactions unconnected layers are independent, a remarkable consequence of the dipole interaction is the appearance of

Scatteringoftwo-dimensionalsolitonsindipolarBose-Einsteincondensates

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R.Nath1,P.Pedri2andL.Santos1

Institutf¨urTheoretischePhysik,LeibnizUniversit¨atHannover,Appelstr.2,D-30167,Hannover,GermanyLaboratoiredePhysiqueTh´eoriqueetMod`elesStatistiques,Universit´eParisSud,91405OrsayCedex,France

WeanalyzethescatteringofbrightsolitonsindipolarBose-Einsteincondensatesplacedinuncon-nectedlayers.Whereasforshort-rangeinteractionsunconnectedlayersareindependent,aremark-ableconsequenceofthedipoleinteractionistheappearanceofnovelnonlocalinterlayere ects.In

particular,weshowthattheinterlayerinteractionleadstoane ectivemolecularpotentialbetweendisconnectedsolitons,inducingacomplexscatteringphysicsbetweenthem,whichincludesinelasticfusionintosoliton-molecules,andstrongsymmetricandasymmetricinelasticresonances.Inad-dition,afundamentallynew2Dscatteringscenarioinmatter-wavesolitonsispossible,inwhichinelasticspiralingoccurs,resemblingphenomenainphotorrefractivematerials.Finally,weconsiderthescatteringofunconnected1Dsolitonsanddiscussthefeasibilityincurrentongoingexperiments.

arXiv:cond-mat/0610703v2 [cond-mat.other] 1 Nov 2006

Uptoveryrecently,typicalexperimentsonultracoldgasesinvolvedparticlesinteractingdominantlyviaashort-rangeisotropicpotential,which,duetotheverylowenergiesinvolved,isfullydeterminedbythecorre-spondings-wavescatteringlength.However,recentex-perimentsoncoldmolecules[1],Rydbergatoms[2],andatomswithlargemagneticmoment[3],openafascinat-ingnewresearcharea,namelythatofdipolargases,forwhichthedipole-dipoleinteraction(DDI)playsasignif-icantorevendominantrole.TheDDIislong-rangeandanisotropic(partiallyattractive),andleadstofundamen-tallynewphysicsincondensatesdegeneratedFermigasesandstrongly-correlatedatomicsystemsItleadstotheEinstein-deHaase ectinspinorcon-densatesandmaybeemployedforcom-putationandultracoldchemistry[11].Recently,time-of- ightexperimentsinChromiumhaveallowedforthe rstobservationeverofdipolare ectsinquantumgasesInterestingly,thephysicsofshort-rangeinteractingBose-Einsteincondensates(BECs)atlowtemperaturesisgivenbyanonlinearSchr¨odingerequation(NLSE)withcubiclocalnonlinearity,similartotheoneappearinginothersystems,inparticularinKerrmediainnonlinearoptics.In1D,nonlinearityallowsforsolitonicsolutionswhichhavebeenobservedinBECHowever,brightsolitonsareunstablein2Dand3D.Inperiodicpotentialsmultidimensionaldiscretesolitonsarepossible[15],buttheydonotmoveinamultidimensionalway,althoughtheuseofopticallatticeshasbeenproposedtomove2Dand3DdiscretesolitonsalongafreedirectionOtherinterestingpossibilitytostabilizehighdimen-sionalsolitonsistouseFeshbachresonancestomanagespatiallyand/ortemporallythescatteringlengthDuetotheDDI,adipolarBECisdescribedbyaNLSEwithnonlocalcubicnonlinearityopeninganin-terestingcross-disciplinarylinkbetweenBECandothernonlocalnonlinearmedia,ase.g.plasmaswherethenonlocalresponseisinducedbyheatingandioniza-tion,andnematicliquidcrystals,whereitistheresultof

long-rangemolecularinteractions[19].Nonlocalityplaysacrucialinthephysicsofsolitonsandmodulationin-stability[20,22].Inparticular,anysymmetricnonlo-calnonlinearresponsewithpositivede niteFourierspec-trumhasbeenmathematicallyshowntoarrestcollapseinarbitrarydimensionsIndeed,multidimensionalsolitonshavebeenexperimentallyobservedinnematicliquidcrystals[19].Recentlyweshowedthatunderreal-isticconditions,2DsolitonsmaybegeneratedindipolarBECHowever,theanisotropiccharacteroftheDDIviolatestheconditionsofRef.andasaconsequenceastabilitywindowoccurs,ratherthanastabilitythresh-oldforasu cientlylargedipolestrength.InRef.[23]webrie ystudiedthescatteringof2Ddipolarsolitons,whichisinelasticcontrarytothe1Dinlo-calNLSE,duetothelackofintegrability[25].However,theanalysisoftheinelasticscatteringwaslargelycom-plicatedbythespatialoverlappingofthesolitons.

Figure1:SchematicrepresentationofthesystemconsideredinthisLetter.

Inthefollowing,weconsiderdipolarBECsplacedindisconnectedlayers(Fig.1).Forthecaseofshort-rangeinteractions,thetwolayersareindependentifthehop-pingissuppressed.AremarkableconsequenceoftheDDIisthatunconnectedlayersbecomecoupledduetonon-localdensity-densityinteractions,leadingtointerestinginterlayere ects,ase.g.thepossibilityofaBECof la-ments,recentlydiscussedinRef.InthisLetter,weanalyzetherichphysicsintroducedbyinterlayere ectsinthenonlinearpropertiesofdipolarBECs.Inparticular,weshowthatthisinterlayerinteractionleadstoane ec-tivemolecularpotentialbetweenfullydisconnectedsoli-

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