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