Oscillations of rotating trapped Bose-Einstein condensates - art. no. 063605

The tensor-virial method is applied for a study of oscillation modes of uni formly rotating Bose-Einstein condensed gases, whose rigid-body rotation is supported by an vortex array. The second-order virial equations are derive d in the hydrodynamic regime for an arbitrary external harmonic trapping po tential assuming that the condensate is a superfluid at zero temperature. T he axisymmetric equilibrium shape of the condensate is determined as a func tion of the deformation of the trap; its domain of stability is bounded by the constraint Omega <1 on the rotation rate (measured in units of the trap frequency <omega>(o)) The oscillations of the axisymmetric condensate are stable with respect to the transverse-shear and toroidal modes of oscillati ons, corresponding to the l=2, \m \ = 1,2 surface deformations. The eigenfr equencies of the modes are real and represent undamped oscillations. The co ndensate is also stable against quasiradial pulsation modes (l=2, m=0), and its oscillations are undamped, if the superflow is assumed incompressible. In the compressible case we find that for a polytropic equation of state, the quasiradial oscillations are unstable when gamma (3 - Omega (2))<1 - 3< Omega>(2), and are stable otherwise. Thus, a dilute Bose gas, whose equatio n of state is polytropic with gamma =2 to leading order in the diluteness p arameter, is stable irrespective of the rotation rate. In nonaxisymmetric t raps, the equilibrium constrains the (dimensionless) deformation in the pla ne orthogonal to the rotation to the domain A(2)>Omega (2) with Omega <l. T he second-harmonic-oscillation modes in nonaxisymmetric traps separate into two classes that have even or odd parity with respect to the direction of the rotation axis. Numerical solutions show that these modes are stable in the parameter domain where equilibrium figures exist.