An experiment to test the discreteness of time

Time at the Planck scale ($\sim 10^{-44}\,\mathrm{s}$) is an unexplored physical regime. It is widely believed that probing Planck time will remain for long an impossible task. Yet, we propose an experiment to test the discreteness of time at the Planck scale and estimate that it is not far removed from current technological capabilities.
Comment: 11 pages, 5 figures, 1 table, published version (re-uploaded to replace all shortDOIs to DOIs, in accordance to CrossRef's policies)