  Driven-dissipative systems in two dimensions can differ substantially from
their equilibrium counterparts. In particular, a dramatic loss of off-diagonal
algebraic order and superfluidity has been predicted to occur due to the
interplay between coherent dynamics and external drive and dissipation in the
thermodynamic limit. We show here that the order adopted by the system can be
substantially altered by a simple, experimentally viable, tuning of the driving
process. More precisely, by considering the long-wavelength phase dynamics of a
polariton quantum fluid in the optical parametric oscillator regime, we
demonstrate that simply changing the strength of the pumping mechanism in an
appropriate parameter range can substantially alter the level of effective
spatial anisotropy induced by the driving laser, and move the system into
distinct scaling regimes. These include: (i) the classic algebraically ordered
superfluid below the Berezinskii-Kosterlitz-Thouless (BKT) transition, as in
equilibrium; (ii) the non-equilibrium, long-wave-length fluctuation dominated
Kardar-Parisi-Zhang (KPZ) phase; and the two associated topological defect
dominated disordered phases caused by proliferation of (iii) entropic BKT
vortex-antivortex pairs or (iv) repelling vortices in the KPZ phase. Further,
by analysing the renormalization group flow in a finite system, we examine the
length scales associated with these phases, and assess their observability in
current experimental conditions.
