A Polarization in a 3 level system

[Malamala]

Hello! I am asking this question from a molecular physics perspective (i.e. diatomic molecule placed in an external electric field), but it's quite general in terms of the formulation. I have a 2 level system (call the levels $\ket{0}$ and $\ket{1}$) that can be connected by an electric field through the Stark interaction. The Hamiltonian of the system is (I call the energies of the 2 levels in the absence of electric field $E_1$ and $E_2$):

$$
\begin{pmatrix}
E_0 & -D_{01}E \\
-D_{01}E & E_1
\end{pmatrix}
$$
with $D_{01} = \braket{0|D|1}$. If I diagonalize this, I get (say for the lowest energy state), something of the form: $\ket{\tilde{0}} = a\ket{0}+b\ket{1}$, with $a^2+b^2=1$. Then, the polarization in the ground state is given by:

$$p = \frac{\braket{\tilde{0}|D|\tilde{0}}}{D_{01}}$$
Thus, for a very small external field, $b$ is very small and the polarization is close to zero, while for a very large field, I have $a=b=\sqrt{2}/2$ and thus the polarization is 1, as expected i.e. the molecule is fully polarized in a large external field. However, if I add a 3rd level, connected to $\ket{1}$ by a dipole interaction, the Hamiltonian becomes:

$$
\begin{pmatrix}
E_0 & -D_{01}E & 0\\
-D_{01}E & E_1 & -D_{12}E \\
0 & -D_{12}E & E_2
\end{pmatrix}
$$
with $D_{12} = \braket{1|D|2}$ (which doesn't need to be equal to $D_{01}$ in general and I also assume that the dipoles are real numbers). Now, the ground state wavefunction is $\ket{\tilde{0}} = a\ket{0}+b\ket{1}+c\ket{2}$, but I am not sure how to define the polarization anymore. I know I still need to take the expectation value: $\braket{\tilde{0}|D|\tilde{0}} = 2abD_{01}+2bcD_{12}$ but I am not sure what to divide this by (the same way I divided by $D_{01}$ before), or if I need a different definition. I know I need to have the same behaviour i.e. close to zero poalrization at low field and close to 1 at high field, but I am not sure how to get this in the case of multiple levels. Thank you!