  Entanglement, a key feature of quantum mechanics, is a resource that allows
the improvement of precision measurements beyond the conventional bound
reachable by classical means. This is known as the standard quantum limit,
already defining the accuracy of the best available sensors for various
quantities such as time or position. Many of these sensors are interferometers
in which the standard quantum limit can be overcome by feeding their two input
ports with quantum-entangled states, in particular spin squeezed states. For
atomic interferometers, Bose-Einstein condensates of ultracold atoms are
considered good candidates to provide such states involving a large number of
particles. In this letter, we demonstrate their experimental realization by
splitting a condensate in a few parts using a lattice potential. Site resolved
detection of the atoms allows the measurement of the conjugated variables atom
number difference and relative phase. The observed fluctuations imply
entanglement between the particles, a resource that would allow a precision
gain of 3.8 dB over the standard quantum limit for interferometric
measurements.
