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

Coherent versus incoherent excitation dynamics in dissipative many-body Rydberg systems