Shape oscillation of a rotating Bose-Einstein condensate

– We present a theoretical and experimental analysis of the transverse monopole mode of a fast rotating Bose-Einstein condensate. The condensate’s rotation frequency is similar to the trapping frequency and the effective confinement is only ensured by a weak quartic potential. We show that the non-harmonic character of the potential has a clear influence on the mode frequency, thus making the monopole mode a precise tool for the investigation of the fast rotation regime. The investigation of rotating gases or liquids is a central issue in the study of superfluids [1,2]. During the recent years, several experiments using rotating atomic Bose-Einstein condensates have provided a spectacular illustration of the notion of quantized vortices [3,4,5,6]. Depending on the rotation frequency of the gas, a single vortex or a regular array of vortices can be observed experimentally. When the rotation frequency is increased to a very large value, a new class of phenomena is predicted, in connection with quantum Hall physics [7, 8, 9, 10, 11, 12, 13, 14]. For a gas confined in a harmonic potential, the fast rotation domain corresponds to stirring frequencies Ω of the order of the trapping frequency ω⊥ in the plane perpendicular to the rotation axis (hereafter denoted z). From a classical point of view, the transverse trapping and centrifugal forces compensate each other for this stirring frequency, and the motion of the particles in the xy plane is only driven by Coriolis and interatomic forces. This situation is similar to that of an electron gas in a magnetic field, since Lorentz and Coriolis forces have the same mathematical structure. In order to approach the regime of fast rotation two paths are currently being explored. The first approach is implemented in a pure harmonic potential and is based on evaporative spin-up, i.e. the selective removal of particles with low angular momentum [15]. The stirring frequency Ω can then be raised close to ω⊥ (Ω = 0.993ω⊥ was reached in [16]). The second approach, which is followed here, consists in adding to the quadratic confinement a small positive quartic potential, which ensures that the particles will remain confined even when Ω exceeds ω⊥ [17,18,19,20,21,22]. We have recently proven that this method can be successfully implemented and we have mechanically stirred a rubidium Bose-Einstein condensate up to Ω ≃ 1.05ω⊥ [23]. All experiments performed so far (including the present one) are still deeply within the mean field regime, characterized by a number of vortices Nv well below the number of particles () LKB is a unité de recherche of Ecole Normale Supérieure and Université Paris 6, associated to the CNRS.