  Bose-Einstein condensate (BEC) is considered under conditions of Feshbach
resonance in two-atom collisions due to a coupling of atomic pair and resonant
molecular states. The association of condensate atoms can form a molecular BEC,
and the molecules can dissociate to pairs of entangled atoms in two-mode
squeezed states. Both entanglement and squeezing can be applied to quantum
measurements and information processing.
  The processes in the atom-molecule quantum gas are analyzed using two
theoretical approaches. The mean-field one takes into account deactivating
collisions of resonant molecules with other atoms and molecules, neglecting
quantum fluctuations. This method allows analysis of inhomogeneous systems,
such as expanding BEC. The non-mean-field approach -- the parametric
approximation -- takes into account both deactivation and quantum fluctuations.
This method allows determination of optimal conditions for formation of
molecular BEC and describes Bose-enhanced dissociation of molecular BEC, as
well as entanglement and squeezing of the non-condensate atoms.
