  Exposing a many-body system to external drives and losses can transform the
nature of its phases and opens perspectives for engineering new properties of
matter. How such characteristics are related to the underlying microscopic
processes of the driven and dissipative system is a fundamental question. Here
we address this point in a quantum gas that is strongly coupled to a lossy
optical cavity mode using two independent Raman drives, which act on the spin
and motional degrees of freedom of the atoms. This setting allows us to control
the competition between coherent dynamics and dissipation by adjusting the
imbalance between the drives. For strong enough coupling, the transition to a
superradiant phase occurs, as is the case for a closed system. Yet, by
imbalancing the drives we can enter a dissipation-stabilized normal phase and a
region of multistability. Measuring the properties of excitations on top of the
out-of-equilibrium phases reveals the microscopic elementary processes in the
open system. Our findings provide prospects for studying squeezing in
non-Hermitian systems, quantum jumps in superradiance, and dynamical spin-orbit
coupling in a dissipative setting.
