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Phase transitions correspond to the singular behavior of physical systems inresponse to continuous control parameters like temperature or external fields.Near continuous phase transitions, associated with the divergence of acorrelation length, universal power-law scaling behavior with criticalexponents independent of microscopic system details is found. Recently,dynamical quantum phase transitions and universal scaling have been predictedand also observed in the non-equilibrium dynamics of isolated quantum systemsafter a quench, with time playing the role of the control parameter. However,signatures of such critical phenomena in time in open systems, whose dynamicsis driven by the dissipative contact to an environment, were so far elusive.Here, we present results indicating that critical scaling with respect to timecan also occur during the relaxation dynamics of an open quantum systemdescribed by mixed states. We experimentally measure the relaxation dynamics ofthe large atomic spin of individual Caesium atoms induced by the dissipativecoupling via spin-exchange processes to an ultracold Bose gas of Rubidiumatoms. For initial states far from equilibrium, the entropy of the spin stateis found to peak in time, transiently approaching its maximum possible value,before eventually relaxing to its lower equilibrium value. Moreover, afinite-size scaling analysis based on numerical simulations shows that itcorresponds to a critical point with respect to time of the dissipative systemin the limit of large system sizes. It is signalled by the divergence of acharacteristic length at a critical time, characterized by critical exponentsthat are found to be independent of system details.

Indication of critical scaling in time during the relaxation of an open quantum system