Multipath interferometer with ultracold atoms trapped in an optical lattice

We study an ultracold gas of N bosons trapped in a one-dimensional M-site optical lattice perturbed by a spatially dependent potential gx(j), where the unknown coupling strength g is to be estimated. We find that the measurement uncertainty is bounded by Delta g alpha 1/N(M-j-1). For a typical case of a linear potential, the sensitivity improves as M-1, which is a result of multiple interferences between the sites, an advantage of multipath interferometers over two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after the action of the potential, the particles are released from the lattice and form an interference pattern. If the parameter is estimated by a least-squares fit of the average density to the interference pattern, the sensitivity still scales like M-1 for linear potentials. We finally discuss the role of useful entanglement of the initial state in the lattice to beat the shot-noise limit. DOI: 10.1103/PhysRevA.87.033607