= Fixed-number two-mode condensate
{title2=$|\chi\rangle=(Ca_0^\dagger+Sa_1^\dagger)^N|0\rangle/\sqrt{N!}$}
All $N$ <bosons> occupy the same normalized one-particle superposition with $|C|^2+|S|^2=1$. Its occupation distribution in the original two modes is binomial, not two independent <Poisson distributions>. In particular, $\langle N_1\rangle=N|S|^2$ and $\langle N_0N_1\rangle=N(N-1)|C|^2|S|^2$. These <factorial moments> give finite-particle corrections to interaction <energies>. The state is also the two-mode realization of a spin <coherent state> with spin $N/2$.
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