  Understanding and probing phase transitions in non-equilibrium systems is an
ongoing challenge in physics. A particular instance are phase transitions that
occur between a non-fluctuating absorbing phase, e.g., an extinct population,
and one in which the relevant order parameter, such as the population density,
assumes a finite value. Here we report the observation of signatures of such a
non-equilibrium phase transition in an open driven quantum system. In our
experiment rubidium atoms in a quasi one-dimensional cold disordered gas are
laser-excited to Rydberg states under so-called facilitation conditions. This
conditional excitation process competes with spontaneous decay and leads to a
crossover between a stationary state with no excitations and one with a finite
number of excitations. We relate the underlying physics to that of an absorbing
state phase transition in the presence of a field (i.e. off-resonant excitation
processes) which slightly offsets the system from criticality. We observe a
characteristic power-law scaling of the Rydberg excitation density as well as
increased fluctuations close to the transition point. Furthermore, we argue
that the observed transition relies on the presence of atomic motion which
introduces annealed disorder into the system and enables the formation of
long-ranged correlations. Our study paves the road for future investigations
into the largely unexplored physics of non-equilibrium phase transitions in
open many-body quantum systems.
