Measurement of the $s$-wave scattering length between metastable helium isotopes

We report the first experimental determination of the interspecies $s$-wave scattering length\,($a_{34}$) between the $2\,^3S_1\,(F=3/2,m_F=3/2)$ state of $^3$He$^*$ and the $2\,^3S_1\,(m_J=1)$ state of $^4$He$^*$. We determine $a_{34}$ by inducing oscillations in a trapped Bose-Einstein condensate of $^4$He$^*$ and measuring the damping rate of these oscillations due to the presence of $^3$He$^*$ atoms. The deduced value of $a_{34}=29\pm3$\,nm is in good agreement with theoretical predictions. The knowledge of this scattering length is important for many fundamental experiments between these helium isotopes.