Stirring a Bose–Einstein condensate

By shining a tightly focused laser light on a Bose–Einstein condensate (BEC) and moving the centre of the beam along a spiral path one may stir the BEC and create vortices. It is shown that one can induce rotation of the BEC in the direction opposite to the direction of stirring. When a spoon, stick or another object of a similar shape is used to stir a liquid, the liquid rotates in the direction induced by the stirring object. Is it possible to make the liquid rotate counterclockwise while stirring it clockwise? The aim of this paper is to show that this counterintuitive scenario may be realized in a quantum fluid, or more precisely a Bose–Einstein condensate (BEC), when stirring it with the help of a tightly focused laser beam. Creation of vortices in a BEC and the study of their properties has recently been the subject of quite intensive research (an extensive list of references may be found in [1]). Vortices have been created in a BEC experimentally using various methods. The Paris group [2] used a rotating anisotropic potential (created by a detuned broad laser beam) to make a direct analogue of the rotating bucket experiments [3]. The formation of a vortex is then the result of dynamical instabilities appearing in the course of the experiment [4]. A similar method was used by Ketterle’s group [5]. The Boulder group [6] created vortices in a two-component condensate, where one fraction was made to rotate with respect to the other by means of the phase engineering technique. The latter technique attempts to create directly the desired vortex state in the condensate. Various ‘stirring’ propositions for the creation of vortices have been discussed theoretically [4, 7]. In particular [7] used a localized potential moving on a circular path (with an appropriate smooth turn-on and turn-off of the stirrer). Such a stirring produces the condensate state which may be approximately described as a time-dependent combination of the ground state and the vortex state. As time evolves the system undergoes a generalized Rabi oscillation between the ground state and the vortex state. Similar in spirit is our recent proposition for the creation of vortices in a BEC [8]. It relies on an appropriate deformation of a harmonic trapping potential by means of an additional, tightly focused laser beam. The beam approaches the centre of the trap moving along a spiral path. The effective interaction of the detuned laser beam with atoms results in an additional 0953-4075/02/194051+07$30.00 © 2002 IOP Publishing Ltd Printed in the UK 4051