By using highly time-resolved spectroscopy with an alternative {sigma}+/{sigma} - laser pulse modulation technique, we are able to measure the fast buildup and decay times of the dynamical nuclear spin polarization (DNSP) at 5 K for a single InAs quantum dot (QD) with positively charged exciton. It is shown that the nuclear dipole-dipole interaction can efficiently depolarize DNSP with a typical time constant of 500 {mu}s in the absence of external magnetic field. By using an external field of 8 mT to suppress the nuclear dipolar interaction, the decay time turns to be mainly induced by interaction with unpaired electron and extends to about 5 ms. In addition, it is found that the time constant of hole-induced depolarization of nuclear spin is about 112 ms.
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