Figure 6

Steady state Wigner functions of the quantum microwave system. Densityplots of steady state Wigner functions of the quantum microwave system forvarious parameter regimes. The Wigner function $W(x,y)$ is plotted wherex and y are two quadratures of the microwave field. Thesenine plots show the quantum steady states that correspond to the parameters ofthe nine black circles in Figure 3. Specifically,from top-left to bottom-right, moving form left to right, then top to bottom,these parameter values are: $({\kappa }^{\prime },{\Delta }^{\prime })=(0,10),(5,10),(0,0),(5,0),(0,-10),\text{ and }(5,-10)$. The otherparameters are set to unity $\chi =\gamma =1$for the purpose of having a Wigner density well inside the number basistruncation. The quantum steady state shows clear signs of the semi-classicalbifurcations it undergoes. Particular comparison can be made to thesemi-classical steady states of Figure 4. Thequantum steady state has support centred on the semi-classical stable fixedpoints.