Towards a test of the universality of free fall using a $^6$Li-$^7$Li atom interferometer

We present a dual species guided matter-wave interferometer for performing a differential measurement of the acceleration of free fall for $^{6}$Li and $^{7}$Li atoms to test the universality of free fall (UFF). Use of this combination of atoms leads to a high sensitivity to new physics because of the relatively large difference difference between $^{6,7}$Li as compared with Be-Ti or $^{85,87}$Rb. An optical lattice will be loaded with $^{6}$Li and $^{7}$Li atoms from a dual species 2D/3D-magneto-optical trap. The lattice will then be employed both as a waveguide to prevent atom losses due to the high thermal velocity of Li and as large-momentum-transfer beam splitters in analogy to the Bloch-Bragg-Bloch beam splitters already developed by us~[1,2]. This allows for high sensitivies as the interferometer's phase shift scales as $k_{\rm{eff}}T^2$, where $\hbar k_{\rm{eff}}$ is the transferred momentum and $T$ the time of evolution between the beam splitters. We anticipate an accuracy of $10^{-14}g$ for the differential acceleration measurement. Systematic effects, in particular gravity gradients, are adressed in our design. Furthermore, novel cooling techniques for Li such as Raman sideband cooling are investigated.\\[4pt] [1] H. M\"{u}ller et al., Phys. Rev. Lett. {\bf 100}, 180405 (2008)\\[0pt] [2] H. M\"{u}ller et al., Phys. Rev. Lett. {\bf 102}, 240403 (2009)