  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.
