Scattering of two-dimensional solitons in dipolar Bose-Einst(4)

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

proposed[27]andexperimentallyobserved[28].Finally,weconsider1DBECsplacedatneighboring1D-sites(x=±x0)ofa2Dlattice,withthedipoleori-entedalongthesiteaxis.Followingsimilarscalingar-gumentsasabove,itispossibletoshowthatforg>0,abrightsolitonispossibleifβ>3/4π.Although,ofcourse,some2Dfeaturesaremissedin1D,itisindeedpossibletoobserveinelasticprocessesalsoin1Dsolitons.Thisisparticularlyrelevantforcurrentexperimentsin52

Cr,sincenotuningisnecessaryfor1Dsolitons,eas-ingverysigni cantlytheexperimentalrequirements.For52

CraFeshbachresonanceisnecessarytosatisfythepre-viouscondition,butFeshbachresonancesarewellchar-acterizedandaccessible[31].InFig.5wedepictanex-ampleofthedynamicsofthesolitonwidthinandoutofresonance,whichclearlyshowsaresonant(althoughnon-destructive)behaviorforintermediatevelocities.Summarizing,interlayere ectsareafundamentallynewfeatureintroducedbytheDDIindipolargasesplacedinunconnectedlayersofanopticallattice.Thesee ectsmayhaveremarkableconsequences,ase.g.theformationofaBECof laments[26].InthisLetter,wediscussedtherichphysicsintroducedbyinterlayere ectsinthenonlinearpropertiesofdipolarBECs,andinpar-ticularinthescatteringofunconnectedsolitons.TheDDIinducesaninelasticsoliton-solitonscattering,thatforlowrelativevelocities,leadstotheinelasticfusionintoasolitonmolecule.Interestingly,theinelasticlossesdonotincreasemonotonicallyfordecreasingrelativeve-locities,butonthecontraryshowstrongresonancesatintermediatevelocities,atwhich,afterinteracting,thesolitonwidthsarestronglymodi ed,eventuallyleadingtosolitondestruction.Thise ectappears,because,duetotherelativelylowexcitationfrequenciesofthesolitons,aresonantcouplingbetweenincomingkineticenergyandinternalsolitonmodesispossibleforlowrelativeveloc-itieswellwithintheinelasticregime.Wehaveshownthatasimilare ectshouldbeobservablein1Dgeome-tries,wheretheexperimentalrequirementsmaybeeasilyful lledinon-goingChromiumexperiments.Finally,wehaveconsideredthe2Dscatteringofdipolarsolitons,auniquepossibilityo eredbythedipolarinteractionsincoldgases.Wehaveshownthatduetothecombina-tionofinelastictrappingandinitialangularmomentumaspiralingmotionispossible,o eringfascinatinglinkstosimilarphysicsinphotorrefractivematerials.ConversationswithY.Kivshar,andT.Pfauareac-knowledged.ThisworkwassupportedbytheDFG(SFB-TR21,SFB407,SPP1116),theMinist`eredellaRecherche(ACINanoscience201),theANR(NT05-2

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