Squeezed vacuum state
= Squeezed vacuum state
{wiki=Squeezed_coherent_state}
The squeezed vacuum is $|\gamma\rangle=S(\gamma)|0\rangle$. Its position and momentum variances are rescaled in opposite directions,
$$
(\Delta X)^2=\frac{\hbar}{2m\omega}e^{-2\gamma},
\qquad
(\Delta P)^2=\frac{m\hbar\omega}{2}e^{2\gamma},
$$
so it remains an <equality case of the Heisenberg uncertainty relation>[minimum-uncertainty state] with $\Delta X\Delta P=\hbar/2$.