  Photon statistics is a powerful tool for characterizing the emission dynamics
of nanoscopic systems and their photophysics. Recent advances that combine
correlation spectroscopy with scanning tunneling microscopy-induced
luminescence (STML) have allowed measuring the emission dynamics from
individual molecules and defects demonstrating their nature as single photon
emitters. The application of correlation spectroscopy to the analysis of the
dynamics of a well-characterized adsorbate system in ultrahigh vacuum remained
to be shown. Here we combine single photon time correlations with STML to
measure the dynamics of individual $H_2$ molecules between a gold tip and a
Au(111) surface. An adsorbed $H_2$ molecule performs recurrent excursions below
the tip apex. We use the fact that the presence of the $H_2$ molecule in the
junction modifies plasmon emission to study the adsorbate dynamics. Using the
$H_2$ molecule as a chopper for STM-induced optical emission intensity we
demonstrate bunching in the plasmonic photon train in a single measurement over
six orders of magnitude in the time domain (from microseconds to seconds) that
takes only a few seconds. Our findings illustrate the power of using photon
statistics to measure the diffusion dynamics of adsorbates with STML.
