In this Thesis, I will report on the experiments performed during my Ph.D. in Pisa. The aim of the thesis is to explore the evolution of a many-body system in a dissipative regime. This can be done by the means of a cold ensemble of Rydberg atoms that, thanks to their peculiar properties, provides a versatile experimental platform to observe non-trivial dynamics of correlated excitations and new phase transitions. The Rydberg-Rydberg mechanical interaction is measured and a deexcitation technique is used to implement a state selective experimental protocol aimed at the measurement of the lifetime. Finally, we use our Rydberg atom system in the dissipative regime to implement a second order absorbing-state phase transition, which arises from the competition between two opposing processes: the correlated excitation and the spontaneous decay to the ground state. Clear signatures of the undergoing phase transition have been measured. These results pave the road for future investigations into the largely unexplored physics of nonequilibrium phase transitions in open many-body quantum systems
