  The gamma-ray burst (GRB) 050904 at z = 6.3 provides the first opportunity of
probing the intergalactic medium (IGM) by GRBs at the epoch of the
reionization. Here we present a spectral modeling analysis of the optical
afterglow spectrum taken by the Subaru Telescope, aiming to constrain the
reionization history. The spectrum shows a clear damping wing at wavelengths
redward of the Lyman break, and the wing shape can be fit either by a damped Ly
alpha system with a column density of log (N_HI/cm^{-2}) ~ 21.6 at a redshift
close to the detected metal absorption lines (z_metal = 6.295), or by almost
neutral IGM extending to a slightly higher redshift of z_{IGM,u} ~ 6.36. In the
latter case, the difference from z_metal may be explained by acceleration of
metal absorbing shells by the activities of the GRB or its progenitor. However,
we exclude this possibility by using the light transmission feature around the
Ly beta resonance, leading to a firm upper limit of z_{IGM,u} < 6.314. We then
show an evidence that the IGM was largely ionized already at z=6.3, with the
best-fit neutral fraction of IGM, x_HI = N_HI/N_H = 0.00, and upper limits of
x_HI < 0.17 and 0.60 at 68 and 95% C.L., respectively. This is the first direct
and quantitative upper limit on x_HI at z > 6. Various systematic uncertainties
are examined, but none of them appears large enough to change this conclusion.
To get further information on the reionization, it is important to increase the
sample size of z >~ 6 GRBs, in order to find GRBs with low column densities
(log N_HI <~ 20) within their host galaxies, and for statistical studies of Ly
alpha line emission from host galaxies.
