Optical generation of vortices in trapped Bose-Einstein condensates

Abstract

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

Vortices in a trapped dilute Bose-Einstein condensate

“…In order to nucleate vortices, the trapped gas can be rotated at temperatures above the BEC transition. Recently, it has been suggested that vorticity could be imprinted by imaging a BEC through an absorption plate [186]. The method consists of passing a far-off-resonant laser pulse through an absorption plate with an azimuthally dependent absorption coefficient, imaging the laser beam onto a BEC, and thus creating the corresponding nondissipative Stark-shift potential and condensate phase shift.…”

“…Also the vortex state can be detected by the splitting of the collective condensate modes in axisymmetric traps [62,111,115] or by looking at the phase slip in the interference fringes produced by two expanding condensates [167,70]. Dobrek et al [186] proposed an interference method to detect vortices by coherently pushing part of the condensate with optically induced Bragg scattering. A detection scheme that reveals the existence of vortex states in a cylindrically symmetric trap is discussed by Goldstein, Wright and Meystre [193].…”

Generation and interaction of solitons in Bose-Einstein condensates

“…In this way one can imprint the desired phase structure on the condensate and hence create a dark soliton [22,23].…”

“…Let us review here how the phase imprinting can lead to the creation of a soliton [22]. For a laser pulse duration shorter than the correlation time of the condensate τ cor =h/µ, where µ is the chemical potential, the wave function acquires a local phase factor e −iφ without changing the condensate's density profile.…”

“…So far the observed solitons in one component BEC's have been generated by the method of phase imprinting. This method, originally proposed to generate vortices, has become a very efficient tool to engineer the phase in condensates [22,23]. Optimization of the phase imprinting method has been recently discussed by Carr et al [24], where initially not only the phase but also the density is properly engineered.…”