  Excitable photonic systems show promise for ultrafast analog computation,
several orders of magnitude faster than biological neurons. Optically injected
quantum dot lasers display several excitable mechanisms with dual state quantum
lasers recently emerging as true all or none excitable artificial neurons. For
use in applications, deterministic triggering is necessary and this has
previously been demonstrated in the literature. In this work we analyse the
crucially important \emph{refractory time} for this dual state system, which
defines the minimum possible time between distinct pulses in any excitable
pulse train. Ultrashort times on the order of 1~ns are obtained suggesting
potential use where ultrafast analog computing is desired.
