  Atom chips provide a versatile `quantum laboratory on a microchip' for
experiments with ultracold atomic gases. They have been used in experiments on
diverse topics such as low-dimensional quantum gases, cavity quantum
electrodynamics, atom-surface interactions, and chip-based atomic clocks and
interferometers. A severe limitation of atom chips, however, is that techniques
to control atomic interactions and to generate entanglement have not been
experimentally available so far. Such techniques enable chip-based studies of
entangled many-body systems and are a key prerequisite for atom chip
applications in quantum simulations, quantum information processing, and
quantum metrology. Here we report experiments where we generate multi-particle
entanglement on an atom chip by controlling elastic collisional interactions
with a state-dependent potential. We employ this technique to generate
spin-squeezed states of a two-component Bose-Einstein condensate and show that
they are useful for quantum metrology. The observed 3.7 dB reduction in spin
noise combined with the spin coherence imply four-partite entanglement between
the condensate atoms and could be used to improve an interferometric
measurement by 2.5 dB over the standard quantum limit. Our data show good
agreement with a dynamical multi-mode simulation and allow us to reconstruct
the Wigner function of the spin-squeezed condensate. The techniques
demonstrated here could be directly applied in chip-based atomic clocks which
are currently being set up.
