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

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.053620· OSTI ID:21528700

Sapina, I; Dahm, T; Schopohl, N ^[1]

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1. Institut fuer Theoretische Physik and Center for Collective Quantum Phenomena, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

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 {epsilon}{sub D{ne}}0 the release energy of the condensate depends on the trap orientation angle {theta}{sub T} between the principal axis e{sub 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 {omega}{sub a} and trap orientation angles {theta}{sub T}. For the special case of a spherical harmonic trap with trap frequency {omega} it is rigorously shown for -(1/2)<{epsilon}{sub D}<1 that a pure s-wave symmetry breather excitation of the condensate density exists, that oscillates at a constant frequency {Omega}{sub s}={radical}(5){omega} 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 {epsilon}{sub D{ne}}0 not isotropic. For {theta}{sub T{ne}}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{sub x}{sup 2}{sub -y}{sup 2}- and d{sub z}{sup 2}-wave, and d{sub xz}-wave symmetry, and two modes that are combinations of basis functions with d{sub yz}- and d{sub xy}-wave symmetry. A characteristic difference in the dependence of the frequencies of these six collective modes on the dipole interaction strength parameter {epsilon}{sub 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{sub s} of the atoms.

• OSTI ID: 21528700
• Journal Information: Physical Review. A, Vol. 82, Issue 5; Other Information: DOI: 10.1103/PhysRevA.82.053620; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
ANISOTROPY
BOSE-EINSTEIN CONDENSATION
DENSITY
DIPOLES
EIGENFREQUENCY
EXCITATION
MAGNETIC FIELDS
PARTICLES
QUANTUM MECHANICS
S WAVES
SCATTERING LENGTHS
SPHERICAL HARMONICS
SPIN ORIENTATION
SYMMETRY
THOMAS-FERMI MODEL
ATOMIC MODELS
DIMENSIONS
ENERGY-LEVEL TRANSITIONS
FUNCTIONS
LENGTH
MATHEMATICAL MODELS
MECHANICS
MULTIPOLES
ORIENTATION
PARTIAL WAVES
PHYSICAL PROPERTIES