  We present deep spectroscopic observations of a Lyman-alpha emitter (LAE)
candidate at z ~ 7.7 using the infrared spectrograph LUCI on the 2 x 8.4m Large
Binocular Telescope (LBT). The candidate is the brightest among the four z ~
7.7 LAE candidates found in a narrow-band imaging survey by Krug et al. 2012.
Our spectroscopic data include a total of 7.5 hours of integration with
LBT/LUCI and are deep enough to significantly (3.2-4.9 sigma) detect the
Lyman-alpha emission line of this candidate, based on its Lyman-alpha flux 1.2
x 10^{-17} erg s^{-1} cm^{-2} estimated from the narrow-band photometry.
However, we do not find any convincing signal at the expected position of its
Lyman-alpha emission line, suggesting that this source is not an LAE at z ~
7.7. The non-detection in this work, together with the previous studies of z ~
7.7 LAEs, puts a strong constraint on the bright-end Lyman-alpha luminosity
function (LF) at z ~ 7.7. We find a rapid evolution of the Lyman-alpha LF from
z ~ 6.5 to 7.7: the upper limit of the z ~ 7.7 LF is more than 5 times lower
than the z ~ 6.5 LF at the bright end (f > 1.0 x 10^{-17} erg s^{-1} cm^{-2},
or L > 6.9 x 10^{42} erg s^{-1}). This is likely caused by an increasing
neutral fraction in the IGM that substantially attenuates Lyman-alpha emission
at z ~ 7.7.
