Steady state Wigner functions of the quantum microwave system. Densityplots of steady state Wigner functions of the quantum microwave system forsmall parameter changes in the blue parameter region of Figure 2. The Wigner function is plotted wherex and y are two quadratures of the microwave field. Theseeight plots show the quantum steady states that correspond to the parameters ofthe eight black crosses in Figure 3. Specificallyfrom left to right these parameter values are: . The otherparameters are set to unity for the purpose of having a Wigner density well inside the number basistruncation. Comparison should be made with the semi-classical steady states ofFigure 5. The quantum steady state shows supportthat shifts from being centred on the semi-classical stable fixed point at theorigin, to being centred on the separated stable pair. This transition does notcorrespond to any semi-classical bifurcation. While the semi-classical steadystates of Figure 5 are quite insensitive to smallparameter shifts in regions bounded by semi-classical bifurcations, thecorresponding quantum steady states have a marked qualitative change.