  We report on optical imaging of the X-ray binary SAX J1808.4-3658 with the
8-m Gemini South Telescope. The binary, containing an accretion-powered
millisecond pulsar, appears to have a large periodic modulation in its
quiescent optical emission. In order to clarify the origin of this modulation,
we obtained three time-resolved $r'$-band light curves (LCs) of the source in
five days. The LCs can be described by a sinusoid, and the long time-span
between them allows us to determine optical period P=7251.9 s and phase 0.671
at MJD 54599.0 (TDB; phase 0.0 corresponds to the ascending node of the pulsar
orbit), with uncertainties of 2.8 s and 0.008 (90 % confidence), respectively.
This periodicity is highly consistent with the X-ray orbital ephemeris. By
considering this consistency and the sinusoidal shape of the LCs, we rule out
the possibility of the modulation arising from the accretion disk. Our study
supports the previous suggestion that the X-ray pulsar becomes rotationally
powered in quiescence, with its energy output irradiating the companion star,
causing the optical modulation. While it has also been suggested that the
accretion disk would be evaporated by the pulsar, we argue that the disk exists
and gives rise to the persistent optical emission. The existence of the disk
can be verified by long-term, multi-wavelength optical monitoring of the source
in quiescence, as an increasing flux and spectral changes from the source would
be expected based on the standard disk instability model.
