Two-mode squeezed vacuum
= Two-mode squeezed vacuum
{title2=$|\Psi\rangle=\operatorname{sech}r\sum_{n\geq0}(e^{i\theta}\tanh r)^n|n,n\rangle$}
Pair creation in two bosonic modes gives the normalized state displayed. The two occupations coincide in each term, while either mode alone has a geometric number distribution. At small $r$, the leading nonvacuum term is a single pair. This optical construction does not require particle-antiparticle modes.