  We analyze the dynamics of quantum statistics in a harmonically trapped
Bose-Einstein condensate, whose two-body interaction strength is controlled via
a Feshbach resonance. From an initially non-interacting coherent state, the
quantum field undergoes Kerr squeezing, which can be qualitatively described
with a single mode model. To render the effect experimentally accessible, we
propose a homodyne scheme, based on two hyperfine components, which converts
the quadrature squeezing into number squeezing. The scheme is numerically
demonstrated using a two-component Hartree-Fock-Bogoliubov formalism.
