Figure 12

The minimum possible noise spectra. The minimum possible noise spectra$S_{{\varphi }_{\min }}(\omega )$ for linearisation about the fixedpoint at the origin for $ϵ=0$.The noise spectrum is dependent on four parameters: the scaled parametricpumping ${\kappa }^{\prime }=\frac{\kappa }{\gamma }$;the scaled detuning ${\Delta }^{\prime }=\frac{\Delta }{\gamma }$;and the scaled probed frequency ${\omega }^{\prime }=\frac{\omega }{\gamma }$and phase ϕ. Here we plot the noise spectrum against only theparametric pumping and the probed frequency. The different coloured sheets showdifferent detunings: the red (innermost) surface shows the noise for nodetuning ${\Delta }^{\prime }=0$;the green (central) surface shows the noise for $|{\Delta }^{\prime }|=1$; and theblue (outermost) surface shows the noise for $|{\Delta }^{\prime }|=2$. Where thesurface is not plotted it is because the origin does not exist as a stablesemi-classical fixed point to be linearised about for those parameter values.We choose the optimal phase ϕ to produce the minimum noise$S_{\varphi }(\omega )$ searching over all frequencies foreach pumping power and detuning.