Entanglement for metrology with atomic ensembles

Ultimate quantum fluctuations which limit the fundamental precision in metrology can be only reduced by entanglement of particles. In particular, squeezing of the fluctuations called the spin projection noise by means of generation of entanglement in an ensemble of atoms can improve the precision of spectroscopy and of atomic clocks. A powerful tool for generation of multiparticle entanglement is a quantum nondemolition measurement (QND). We will describe the fundamentals of QND measurement of atomic collective state with light and present a recent experiment where this method has been used to reduce the projection noise on the clock transition in an ensemble of 10⁵ cold and trapped cesium atoms. Another method for generation of spin squeezing via electron-nucleus entanglement applicable only for atoms with angular momentum higher than 1/2 will be also discussed.