  In order to understand quantum decoherence of a quantum system due to its
interaction with a large system behaving classically, we introduce the concept
of adiabatic quantum entanglement based on the Born-Oppenhemeir approximation.
In the adiabatic limit, it is shown that the wave function of the total system
formed by the quantum system plus the large system can be factorized as an
entangled state with correlation between adiabatic quantum states and
quasi-classical motion configurations of the large system. In association with
a novel viewpoint about quantum measurement, which has been directly verified
by most recent experiments [e.g, S. Durr et.al, Nature 33, 359 (1998)], it is
shown that the adiabatic entanglement is indeed responsible for the quantum
decoherence and thus it can be regarded as a "clean" quantum measurement when
the large system behaves as a classical object. The large system being taken
respectively to be a macroscopically distinguishable spatial variable, a high
spin system and a harmonic oscillator with a coherent initial state, three
illustrations are present with their explicit solutions in this paper.
