  We present a unified view of the Berry phase of a quantum system and its
entanglement with surroundings. The former reflects the nonseparability between
a system and a classical environment as the latter for a quantum environment,
and the concept of geometric time-energy uncertainty can be adopted as a
signature of the nonseparability. Based on this viewpoint, we study their
relationship in the quantum-classical transition of the environment, with the
aid of a spin-half particle (qubit) model exposed to a quantum-classical hybrid
field. In the quantum-classical transition, the Berry phase has a similar
connection with the time-energy uncertainty as the case with only a classical
field, whereas the geometric phase for the mixed state of the qubit exhibits a
complementary relationship with the entanglement. Namely, for a fixed
time-energy uncertainty, the entanglement is gradually replaced by the mixed
geometric phase as the quantum field vanishes. And the mixed geometric phase
becomes the Berry phase in the classical limit. The same results can be draw
out from a displaced harmonic oscillator model.
