After calculating their photon-number variance I tried to compute their second order coherence function, but it turns out larger than 3, implying it is a classical state. Is it wrong? I expected it to be less than 1, thus proving it is a non-classical state.
After finding:
$$ \langle\hat{a}^{\dagger} \hat{a}\rangle=\sinh(r)^2 $$ $$ \langle\hat{a}^{\dagger} \hat{a}^{\dagger} \hat{a}\hat{a}\rangle = \cosh(r)^2 \sinh(r)^2+2\sinh(r)^4 $$
I calculated
$$ g^{(2)}(\tau)=\frac{\langle\hat{a}^{\dagger} \hat{a}^{\dagger} \hat{a}\hat{a}\rangle}{\langle\hat{a}^{\dagger} \hat{a}\rangle^2} =\frac{1+\sinh(r)^2 + 2sinh(r)^2}{\sinh(r)^2} = 3 + \frac{1}{\sinh(r)^2} $$
