= Two excited atoms in a resonant Tavis-Cummings mode
For two equally coupled atoms initially in $|ee;0\rangle$, excitation conservation confines the <interaction picture> to $|ee;0\rangle$, $(|eg\rangle+|ge\rangle)|1\rangle/\sqrt2$ and $|gg;2\rangle$. The <Hamiltonian operator> divided by $\hbar$ has off-diagonal entries $\sqrt2g$ and $2g$. Its <eigenvalues> are $0,\pm\sqrt6g$, so the amplitudes are $(2+\cos\sqrt6gt)/3$, $-i\sin(\sqrt6gt)/\sqrt3$ and $\sqrt2(\cos\sqrt6gt-1)/3$. An ideal one-<photon number> projection therefore heralds a symmetric atomic <Bell state> with probability $\sin^2(\sqrt6gt)/3$, at most $1/3$.
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