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

No abstract

We derive the phase diagram for ultracold trapped dipolar Fermi gases. Below the critical value of the dipole-dipole interaction energy, the BCS transition into a superfluid phase ceases to exist. The critical dipole strength is obtained as a function of the trap aspect ratio. Alternatively, for a given dipole strength there is a critical value of the trap anisotropy for the BCS state to appear. The order parameter exhibits a novel nonmonotonic behavior at the criticality.

We present a review of recent results concerning the physics of ultracold trapped dipolar gases. In particular, we discuss the Bose-Einstein condensation for dipolar Bose gases and the BCS transition for dipolar Fermi gases. In both cases we stress the dominant role of the trap geometry in determining the properties of the system. We present also results concerning bosonic dipolar gases in optical lattices and the possibility of obtaining variety of different quantum phases in such case. Finally, we analyze various possible routes towards achieving ultracold dipolar gases.

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