  We study the impact of dephasing on the excitation dynamics of a cloud of
ultracold two-level Rydberg atoms for both resonant and off-resonant laser
excitation, using the wave function Monte Carlo (MCWF) technique. We find that
while for resonant laser driving, dephasing mainly leads to an increase of the
Rydberg population and a decrease of the Mandel Q parameter, at off-resonant
driving strong dephasing toggles between direct excitation of pairs of atoms
and subsequent excitation of single atoms, respectively. These two excitation
mechanisms can be directly quantified via the pair correlation function, which
shows strong suppression of the two-photon resonance peak for strong dephasing.
Consequently, qualitatively different dynamics arise in the excitation
statistics for weak and strong dephasing in off-resonant excitation. Our
findings show that time-resolved excitation number measurements can serve as a
powerful tool to identify the dominating process in the system's excitation
dynamics.
