The states which have a classical limit are *coherent states* which, for each mode $k$, are of the form $|z\rangle =e^{-|z|^2/2}e^{z \hat a_k^\dagger}|0\rangle$. These have
$$
\hat a_k|z\rangle= z|z\rangle,
$$ 
and hence
$$
\langle z |\hat a_k|z\rangle = z.
$$