product state $\ket{2,2}$ at the avoided crossing, and $\xi_{\textsc{svne}}$ drops to zero in this case, as expected.

In , we plot the correlation between various indicators and $\xi_{\textsc{svne}}$. For this purpose, $80$ values of each of the $\xi$-indicators were calculated with $g$ varied in the range $[-1,1.4]$ in steps of $0.03$. Treating these as sets of random numbers, we obtain the PCC between the various indicators and $\xi_{\textsc{svne}}$, as described in the foregoing. The performance of the entanglement indicators in this case is similar to that found in the BEC system. Increasing $\gamma$ marginally decreases the efficacy of all the indicators.

![Correlation of $\xi_{\textsc{svne}}$ with $\xi$-indicators (left), with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=\frac{1}{2}\pi$ (centre), and with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=0$ (right), for the eigenstates $\ket{\phi_{4,k}}, 
 \,0 \leqslant k \leqslant 4$ in the atom-field interaction model. $\omega_{\mathrm{f}}=\omega_{\mathrm{a}}=
 \gamma=1$.[]{data-label="fig:CorrPlotN4agarwalVaryLambda"}](correlation_matrix_plot_4_agarwal_vary_lambda_U_1_mult.eps "fig:"){width="30.00000%"} ![Correlation of $\xi_{\textsc{svne}}$ with $\xi$-indicators (left), with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=\frac{1}{2}\pi$ (centre), and with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=0$ (right), for the eigenstates $\ket{\phi_{4,k}}, 
 \,0 \leqslant k \leqslant 4$ in the atom-field interaction model. $\omega_{\mathrm{f}}=\omega_{\mathrm{a}}=
 \gamma=1$.[]{data-label="fig:CorrPlotN4agarwalVaryLambda"}](correlation_matrix_plot_4_agarwal_vary_lambda_U_1_xp.eps "fig:"){width="30.00000%"} ![Correlation of $\xi_{\textsc{svne}}$ with $\xi$-indicators (left), with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=\frac{1}{2}\pi$ (centre), and with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=0$ (right), for the 