  We analyze the origin of the intrinsic timing jitter in superconducting
nanowire single photon detectors (SNSPDs) in terms of fluctuations in the
latency of the detector response, which is determined by the microscopic
physics of the photon detection process. We demonstrate that fluctuations in
the physical parameters which determine the latency give rise to the intrinsic
timing jitter. We develop a general description of latency by introducing the
explicit time dependence of the internal detection efficiency. By considering
the dynamic Fano fluctuations together with static spatial inhomogeneities, we
study the details of the connection between latency and timing jitter. We
develop both a simple phenomenological model and a more general microscopic
model of detector latency and timing jitter based on the solution of the
generalized time-dependent Ginzburg-Landau equations for the 1D hotbelt
geometry. While the analytical model is sufficient for qualitative
interpretation of recent data, the general approach establishes the framework
for a quantitative analysis of detector latency and the fundamental limits of
intrinsic timing jitter. These theoretical advances can be used to interpret
the results of recent experiments measuring the dependence of detection latency
and timing jitter on photon energy to the few-picosecond level.
