  Single atoms form a model system for understanding the limits of single
photon detection. Here, we develop a non-Markov theory of single-photon
absorption by a two-level atom to place limits on the absorption (transduction)
time. We show the existence of a finite rise time in the probability of
excitation of the atom during the absorption event which is infinitely fast in
previous Markov theories. This rise time is governed by the bandwidth of the
atom-field interaction spectrum and leads to a fundamental jitter in
time-stamping the absorption event. Our theoretical framework captures both the
weak and strong atom-field coupling regimes and sheds light on the spectral
matching between the interaction bandwidth and single photon Fock state pulse
spectrum. Our work opens questions whether such jitter in the absorption event
can be observed in a multi-mode realistic single photon detector. Finally, we
also shed light on the fundamental differences between linear and nonlinear
detector outputs for single photon Fock state vs. coherent state pulses.
