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

M. Egorov; B. Opanchuk; P. Drummond; B. V. Hall; P. Hannaford; A. I. Sidorov

doi:10.1103/PhysRevA.87.053614

paper

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

arXiv:1204.1591 · doi:10.1103/PhysRevA.87.053614

Abstract

We use collective oscillations of a two-component Bose-Einstein condensate (2CBEC) of \Rb atoms prepared in the internal states $∣ 1 ⟩ \equiv ∣ F = 1, m_{F} = - 1 ⟩$ and $∣ 2 ⟩ \equiv ∣ F = 2, m_{F} = 1 ⟩$ for the precision measurement of the interspecies scattering length $a_{12}$ with a relative uncertainty of $1.6 \times 1 0^{- 4}$ . 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 $a_{12} / a_{11}$ , where $a_{11}$ is the intra-species 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 a reasonable agreement with the theoretical prediction $a_{12} = 98.13 (10) a_{0}$ but deviates significantly from the previously measured value $a_{12} = 97.66 a_{0}$ \cite{Mertes07} which is commonly used in the characterisation of spin dynamics in degenerate \Rb 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 $a_{22} = 95.0 a_{0}$ \cite{Mertes07}. We characterise two-body losses for the component 2 and obtain the loss coefficients $γ_{12} = 1.51 (18) \times 1 0^{- 14} cm^{3} / s$ and $γ_{22} = 8.1 (3) \times 1 0^{- 14} cm^{3} / s$ .

11 pages, 8 figures

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

Abstract

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