Optical lattice clock with atoms confined in a shallow trap

We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunnelling leads to a residual sensitivity to the atom dynamics hence requiring large depths ($50$ to $100\\,E_r$ for Sr) to avoid any frequency shift or line broadening of the atomic transition at the $10^{-17}-10^{-18}$ level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g. higher order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunnelling. We show that using the Earth\'s gravity, much shallower traps (down to $5\\,E_r$ for Sr) can be used for the same accuracy goal