  A combined study with use of time-domain pump-probe spectroscopy and
time-domain terahertz transmission spectroscopy have been carried out on an
underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+{\delta}}$ thin film. It was observed that
the low energy multi-excitation states were decomposed into superconducting gap
and pseudogap. The pseudogap locally opens below $T^*{\simeq}210$ K
simultaneously with the appearance of the high-frequency partial pairs around
1.3 THz. With decreasing temperature, the number of the local domains with the
partial phase coherence increased and saturated near 100 K, and the macroscopic
superconductivity appeared below 76 K through the superconductivity fluctuation
state below 100 K. These experimental results indicate that the pseudogap makes
an important role for realization of the superconductivity as a precursor to
switch from the partial to the macroscopic phase coherence.
