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

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