W e dem onstrate num eri cal l y the e ci ent generati on of vorti ces i n B ose-Ei nstei n condensates (B EC ) by usi ng a \phase i m pri nti ng" m ethod. T he m ethod consi st of passi ng a far o resonant l aser pul se through an absorpti on pl ate w i th azi m uthal l y dependent absorpti on coe ci ent,i m agi ng the l aserbeam onto a B EC ,and thuscreati ng the correspondi ng non-di ssi pati ve Stark shi ftpotenti al and condensate phase shi ft. In ourcal cul ati onsw e take i nto accountexperi m entali m perfecti ons. W e al so propose an i nterference m ethod to detectvorti ces by coherentl y pushi ng partofthe condensate usi ng opti cal l y i nduced B ragg scatteri ng. 03. 75. Fi ,32. 80. Pj,42. 50. V k O ne of the rem ai ni ng chal l enges of the physi cs of trapped B ose-Ei nstei n condensates (B EC ) [ 1{4] , concernsthe dem onstrati on ofthei rsuper ui d behavi or.Super ui di ty i s i nevi tabl y rel ated to the exi stence of vorti ces and persi stent currents i n B EC ,w hi ch so far have not been observed experi m ental l y,despi te seri ous e orts [ 5] .T wo aspectsofthe vortex probl em havebeen studi ed i ntensi vel y:i )i n rotati ng trapsvorti cesappeari n a naturalway as therm odynam i c ground states w i th quanti zed angul arm om entum [ 6] .Stabi l i ty and otherproperti esof vorti ces i n rotati ng traps have been throughl y di scussed i n R ef.[ 7{9] ;i i ) i n stati onary traps creati on ofvorti ces (or rel ated dark sol i tons i n 1D ) requi res the use of dynam icalm eans,and an i ndependent stabi l i ty anal ysi s.Several m ethods were proposed to generate vorti ces i n non-rotati ng traps: sti rri ng the condensate usi ng a bl ue detuned l aser [ 10, 11] , or several l aser beam s [ 12] ; adi abati c passage [ 13] or R am an transi ti ons [ 14] i n bicondensate system s. Such vorti ces are typi cal l y not stabl e,and can exhi bi tdynam i calorenergeti ci nstabi l i ty.In the rstcasevorti cesdecay rapi dl y,i n thesecond thevorti ces are stabl e w i thi n the fram ework ofthe m ean el d theory, and thei r correspondi ng decay requi res to take i nto account i nteracti ons of the B EC w i th the therm al cl oud. In the l attercase the vortex dynam i csi sexpected to besu ci entl y sl ow ,and thusexperi m ental l y accessi bl e [ 15] .In thi sC om m uni cati on we propose and i nvesti gate yet anotherprocedure ofvortex generati on usi ng \phase i mpri nti ng". T hi s m ethod consi sts of i ) passi ng a far o resonant l aser pul se through an absorpti on pl ate w hose absorpti on coe ci ent depends on the rotati on angl e ' around the propagati on axi s and i i ) creati ng the correspondi ng Stark shi ft potenti ali nsi de a B EC by i m agi ng the l aser pul se onto the condensate w hi ch l eads to a ' dependent phase shi ft i n the condensate wave functi on. T hi s m ethod i s very e ci ent and robust,and al l ow s for 1