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

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].…”

“…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.…”

Quantized Vortices in Atomic Bose-Einstein Condensates

“…When the laser intensity is much stronger than the other terms and the duration of the pulse τ is sufficiently short, the evolution of the phase is governed by θ(r, t) = − −1 τ 0 dtV las (r, t). Since the potential amplitude of V las is proportional to the laser intensity, a suitable spatial variation of the intensity can imprint the phase into the condensate (Andrelczyk 2001). This phase-imprinting technique has been used to create a dark soliton (Burger 1999, Denschlag 2000, which is a topological excitation with a complete density dip across which the phase changes by π.…”

“…Several ideas for the creation of vortices by this technique have been proposed theoretically, based on the coherent control of the time evolution of the wave function, instead of mechanical rotation (Marzlin 1997, 1998, Dum 1998, Williams 1999, Nakahara 2000, Andrelczyk 2001, Damski 2001, Nandi 2004, Kapale 2005, Möttönen 2003). …”

Searches for black holes: the recent data

“…So, the effect of the pulse is a sudden phase imprint on each single-particle orbital, according to the pattern written in the plate. The details of this technique are thoroughly discussed in [8,9] for bosons and repeated in [10,11] for fermions. It is worth stressing that this method has already been experimentally realized for the generation of solitons in the Bose-Einstein condensate [12,13].…”