Quantum Enhanced Cavity QED Interferometer with Partially Delocalized Atoms in Lattices*

We propose a quantum enhanced interferometric protocol for gravimetry and force sensing using cold atoms in an optical lattice supported by a standing-wave cavity. By loading the atoms in partially delocalized Wannier-Stark states, it is possible to cancel the undesirable inhomogeneities arising from the mismatch between the lattice and cavity fields and to generate spin squeezed states via a uniform one-axis twisting model. The quantum enhanced sensitivity of the states combined with subsequent implementation of a compound pulse sequence, that allows to separate atoms by several lattice sites, together with the capability to load small atomic clouds in the lattice at micrometric distances from a surface, make our setup ideal for sensing short-range forces. We show that for arrays of 10⁴ atoms, our protocol can reduce the required averaging time by a factor of 10 compared to current lattice-based interferometers after accounting for major sources of decoherence.