Figure 3

‘Phase diagram’ of the semi-classical system. The‘phase diagram’ of the semi-classical system. The existence andcomponents of the semi-classical fixed points are functions of the twonon-dimensional ratios of the parametric pumping magnitude κ,detuning Δ, and dissipation rate γ of the system:${\kappa }^{\prime }=\frac{\kappa }{\gamma }$and ${\Delta }^{\prime }=\frac{\Delta }{\gamma }$.We also show the parameter regimes chosen for numerically computing the quantumsteady state. There are three different classes of fixed points: the origin isa fixed point for all parameter values (stable in the green and striped blueregions, and unstable in the checkered red region); a stable pair of antipodalfixed points exists for ‘above threshold’ parametric pumping (thestriped blue and checkered red regions); and an unstable pair exists for smallvalues of ‘above threshold’ parametric pumping if the detuningΔ is negative (the striped blue region only). Thesemi-classical steady states at the specific various black circles and crossesare depicted in Figures 4 and 5 respectively. These are for comparison with the quantum steadystates discussed in Section 4 and depicted in Figures 4 and 5.