  By making the second quantization for the Cini Model of quantum measurement
without wave function collapse [M. Cini, Nuovo Cimento, B73 27(1983)], the
second order quantum decoherence (SOQD) is studied with a two mode boson system
interacting with an idealized apparatus composed by two quantum oscillators. In
the classical limit that the apparatus is prepared in a Fock state with a very
large quantum number, or in a coherent state with average quantum numbers large
enough, the SOQD phenomenon appears similar to the first order case of quantum
decoherence.
