An atom interferometer offers means to measure physical constants and physical quantities with a high precision, with relatively low cost and convenience as a table-top experiment. A precision measurement of a gravitational acceleration can test fundamental physics concepts such as Einstein equivalence principle (EEP). We identified that the two lithium isotopes (${}^{7}$Li and ${}^{6}$Li) have an advantage for the test of EEP, according to the standard model extension (SME). We aim to build the world's first lithium atom interferometer and test the Einstein equivalence principle.\
We demonstrate a new laser cooling method suitable for a lithium atom interferometer. Although lithium is often used in ultra-cold atom experiments for its interesting physical properties and measurement feasibility, it is more difficult to laser cool lithium than other alkali atoms due to its unresolved hyperfine states, light mass (large recoil velocity) and high temperature from the oven. Typically, standard laser cooling techniques such as Zeeman slowers and magneto-optical traps are used to cool lithium atoms to about 1 mK, and the evaporative cooling method is used to cool lithium atoms to a few $\mu$K for Bose-Einstein condensate (BEC) experiments. However, for the atom interferometry purpose, the evaporative cooling method is not ideal for several reasons: First, its cooling efficiency is so low (0.01 \% or less) that typically only $10^4-10^5$ atoms are left after cooling when one begins with $10^9$ atoms. More atoms in an atom interferometer are needed to have a better signal to noise ratio. Second, an evaporative cooling is used to make a BEC, but we do not need a BEC to make an atom interferometer. In an atom interferometer, a high density of atoms as in a BEC should be avoided since it causes a phase shift due to atom interactions. Third, a setup for an evaporative cooling requires intricate RF generating coils or a high power laser. \
With a simple optical lattice and a moderate laser power (100 mW), we achieved a sub-Doppler cooling of lithium by a new laser cooling method despite the fact that lithium has un-resolved hyperfine structure. We identified that the Sisyphus cooling and the adiabatic cooling mechanisms cooperate and give both lower temperature and higher cooling efficiency than the result that can be achieved by each alone. We cooled ${}^{7}$Li atoms to $\sim \;50\;\mu$K (about 8 times the recoil temperature) in a one dimensional lattice with cooling efficiency of $50\%$. In three dimensions the cooling temperature was limited to $90\,\mu$K due to instability of our 3D lattice, however the same principle applies and potentially a lower temperature can be achieved in 3D as well.
