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 87Rb atoms prepared in the internal states |1〉≡|F=1,mF=−1〉 and |2〉≡|F=2,mF=1〉 for the precision measurement of the interspecies scattering length a12 with a relative uncertainty of 1.6×10−4. 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) Schrödinger equation for an effective harmonic oscillator. The frequency of the collective oscillations is defined by the axial trap frequency and the ratio a12/a11, where a11 is the intraspecies scattering length of a highly populated component 1 and is largely decoupled from the scattering length a22, 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 a12=98.006 (16) a0, where a0 is the Bohr radius. Our reported value is in reasonable agreement with the theoretical prediction a12=98.13 (10) a0 but deviates significantly from the previously measured value a12=97.66a0 [ Phys. Rev. Lett. 99 190402 (2007)] which is commonly used in the characterization of spin dynamics in degenerate 87Rb atoms. Using Ramsey interferometry of the 2CBEC we measure the scattering length a22=95.44 (7) a0 which also deviates from the previously reported value a22=95.0a0 [ Phys. Rev. Lett. 99 190402 (2007)]. We characterize two-body losses for component 2 and obtain the loss coefficients γ12=1.51 (18)×10−14 cm3/s and γ22=8.1 (3)×10−14 cm3/s.