  Open quantum systems exhibit a range of novel out-of-equilibrium behavior due
to the interplay between coherent quantum dynamics and dissipation. Of
particular interest in these systems are driven, dissipative transitions, the
emergence of dynamical phases with novel broken symmetries, and critical
behavior that lies beyond the conventional paradigms of Landau-Ginzburg
phenomenology. Here, we consider a parametrically driven two-mode system in the
presence of non-Markovian system-reservoir interactions. We show that
non-Markovianity modifies the phase diagram of this system resulting in the
emergence of a novel broken symmetry phase in a new universality class that has
no counterpart in a Markovian or equilibrium system. Such reservoir-engineered
dynamical phases can potentially shed light on universal aspects of dynamical
phase transitions in a wide range of non-equilibrium systems, and aid in the
development of techniques for the robust generation of entanglement and quantum
correlations at finite temperatures with potential applications to quantum
metrology.
