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 $2{}^3{S}_1(F=3\mathrm{/}2,m_F=3\mathrm{/}2)$ state of ${}^3$He${}^{\ast }$ and the $2{}^3{S}_1(m_J=1)$ state of ${}^4$He${}^{\ast }$. We determine $a_{34}$ by inducing oscillations in a trapped Bose-Einstein condensate of ${}^4$He${}^{\ast }$ and measuring the damping rate of these oscillations due to the presence of ${}^3$He${}^{\ast }$ atoms. The deduced value of $a_{34}=29\pm 3$,nm is in good agreement with theoretical predictions. The knowledge of this scattering length is important for many fundamental experiments between these helium isotopes.