Ground-state and collective modes of a spin-polarized dipolar Bose-Einstein condensate in a harmonic trap

We report results for the Thomas-Fermi ground state of a spin-polarized dipolar interacting Bose-Einstein condensate for the case when the external magnetic field B is not orientated parallel to a principal axis but is aligned parallel to a symmetry plane of a harmonic anisotropic trap. For a dipole interaction strength parameter ɛ_D≠0 the release energy of the condensate depends on the trap orientation angle ϑ_T between the principal axis e_z,T of the trap and the field B. From the quasiclassical Josephson equation of macroscopic quantum physics we determine the low-lying eigenfrequencies of small-amplitude collective modes of the condensate density for various trap frequencies ω_a and trap orientation angles ϑ_T. For the special case of a spherical harmonic trap with trap frequency ω it is rigorously shown for -(1)/(2)<ɛ_D<1 that a pure s-wave symmetry breather excitation of the condensate density exists, that oscillates at a constant frequency Ω_s=5ω around the ground-state cloud, despite the well-known fact that the shape of the ground-state cloud of a spin-polarized dipolar condensate is for ɛ_D≠0 not isotropic. For ϑ_T≠0 the small-amplitude modes of the particle density with isotropic and quadrupolar symmetry consist of two groups. There exist four modes that are combinations of basis functions, with s-wave, d_x²-y²- and d_z²-wave, and d_xz-wave symmetry, and two modes that are combinations of basis functions with d_yz- and d_xy-wave symmetry. A characteristic difference in the dependence of the frequencies of these six collective modes on the dipole interaction strength parameter ɛ_D for prolate and oblate harmonic triaxial traps, respectively, is suggested to be used as an experimental method to measure the s-wave scattering length a_s of the atoms.