Squeezed-vacuum photon-number moments
= Squeezed-vacuum photon-number moments
{title2=$\langle N^2\rangle=3s^2+2s,\quad\operatorname{Var}N=2s(s+1)$}
Here $s=\sinh^2r$. The pair moment is $\langle N(N-1)\rangle=3s^2+s$. These expressions follow from the single-mode <Bogoliubov transformation> or by differentiating the even-occupation <probability> generating function $G(t)=[\cosh r\sqrt{1-t^2\tanh^2r}]^{-1}$.