Measurement of s-wave scattering lengths in a two-component Bose-Einstein condensate

We use collective oscillations of a two-component Bose-Einstein condensate (2CBEC) of Rb-87 atoms prepared in the internal states vertical bar 1 > equivalent to vertical bar F = 1, m(F) = -1 > and vertical bar 2 > = vertical bar F = 2, m(F) = 1 > for the precision measurement of the interspecies scattering length a(12) with a relative uncertainty of 1.6 x 10(-4). We show that in a cigar-shaped trap the three-dimensional (3D) dynamics of a component with a small relative population can be conveniently described by a one-dimensional (1D) Schrodinger equation for an effective harmonic oscillator. The frequency of the collective oscillations is defined by the axial trap frequency and the ratio a(12)/a(11), where a(11) is the intraspecies scattering length of a highly populated component 1 and is largely decoupled from the scattering length a(22), the total atom number and loss terms. By fitting numerical simulations of the coupled Gross-Pitaevskii equations to the recorded temporal evolution of the axial width we obtain the value a(12) = 98.006 (16) a(0), where a(0) is the Bohr radius. Our reported value is in reasonable agreement with the theoretical prediction a(12) = 98.13 (10) a(0) but deviates significantly from the previously measured value a(12) = 97.66a(0) [Phys. Rev. Lett. 99, 190402 (2007)] which is commonly used in the characterization of spin dynamics in degenerate Rb-87 atoms. Using Ramsey interferometry of the 2CBEC we measure the scattering length a(22) = 95.44 (7) a(0) which also deviates from the previously reported value a(22) = 95.0a(0) [Phys. Rev. Lett. 99, 190402 (2007)]. We characterize two-body losses for component 2 and obtain the loss coefficients gamma(12) = 1.51 (18) x 10(-14) cm(3)/s and gamma(22) = 8.1 (3) x 10(-14) cm(3)/s.