We conducted a deep narrowband NB973 (FWHM = 200 A centered at 9755 A) survey of z=7 Lyman alpha emitters (LAEs) in the Subaru/XMM-Newton Deep Survey Field, using the fully depleted CCDs newly installed on the Subaru Telescope Suprime-Cam, which is twice more sensitive to z=7 Lyman alpha at ~ 1 micron than the previous CCDs. Reaching the depth 0.5 magnitude deeper than our previous survey in the Subaru Deep Field that led to the discovery of a z=6.96 LAE, we detected three probable z=7 LAE candidates. Even if all the candidates are real, the Lyman alpha luminosity function (LF) at z=7 shows a significant deficit from the LF at z=5.7 determined by previous surveys. The LAE number and Lyman alpha luminosity densities at z=7 is ~ 7.7-54% and ~5.5-39% of those at z=5.7 to the Lyman alpha line luminosity limit of L(Ly-alpha) >~ 9.2 x 10^{42} erg s^{-1}. This could be due to evolution of the LAE population at these epochs as a recent galaxy evolution model predicts that the LAE modestly evolves from z=5.7 to 7. However, even after correcting for this effect of galaxy evolution on the decrease in LAE number density, the z=7 Lyman alpha LF still shows a deficit from z=5.7 LF. This might reflect the attenuation of Lyman alpha emission by neutral hydrogen remaining at the epoch of reionization and suggests that reionization of the universe might not be complete yet at z=7. If we attribute the density deficit to reionization, the intergalactic medium (IGM) transmission for Lyman alpha photons at z=7 would be 0.4 <= T_{Ly-alpha}^{IGM} <= 1, supporting the possible higher neutral fraction at the earlier epochs at z > 6 suggested by the previous surveys of z=5.7-7 LAEs, z ~ 6 quasars and z > 6 gamma-ray bursts.
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