The minimum possible noise spectra. The minimum possible noise spectra for linearisation about the fixedpoint at the origin for .The noise spectrum is dependent on four parameters: the scaled parametricpumping ;the scaled detuning ;and the scaled probed frequency 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 ;the green (central) surface shows the noise for ; and theblue (outermost) surface shows the noise for . 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 searching over all frequencies foreach pumping power and detuning.