  We present high signal-to-noise ratio Keck ESI spectra of the two quasars
known to have Gunn-Peterson absorption troughs, SDSS J1030+0524 (z=6.28) and
SDSS J1148+5251 (z=6.37). The Ly alpha and Ly beta troughs for SDSS J1030+0524
are very black and show no evidence for any emission over a redshift interval
of ~0.2 starting at z=6. On the other hand, SDSS J1148+5251 shows a number of
emission peaks in the Ly beta Gunn-Peterson trough along with a single weak
peak in the Ly alpha trough. The Ly alpha emission has corresponding Ly beta
emission, suggesting that it is indeed a region of lower optical depth in the
intergalactic medium at z=6.08.
  The stronger Ly beta peaks in the spectrum of SDSS J1148+5251 could
conceivably also be the result of "leaks" in the IGM, but we suggest that they
are instead Ly alpha emission from an intervening galaxy at z=4.9. This
hypothesis gains credence from a strong complex of C IV absorption at the same
redshift and from the detection of continuum emission in the Ly alpha trough at
the expected brightness. If this proposal is correct, the quasar light has
probably been magnified through gravitational lensing by the intervening
galaxy. The Stromgren sphere observed in the absorption spectrum of SDSS
J1148+5251 is significantly smaller than expected based on its brightness,
which is consistent with the hypothesis that the quasar is lensed.
  If our argument for lensing is correct, the optical depths derived from the
troughs of SDSS J1148+5251 are only lower limits (albeit still quite strong,
with tau(LyA)>16 inferred from the Ly beta trough.) The Ly beta absorption
trough of SDSS J1030+0524 gives the single best measurement of the IGM
transmission at z>6, with an inferred optical depth tau(LyA)>22.
