Figure 1

The ground-state energy $E$ (measured in units of $\hslash \omega$) of the ground state of the DM with $N=4$ atoms as a function of the scaled coupling parameter $\kappa /\omega$. We plot three lines corresponding to different Hamiltonians associated with the DM: the black solid line is related to the energy of $H_0$, the red dashed line corresponds to $H_1$, and the blue dotted line corresponds to $H_2$ (in this case, we consider $\lambda =1,7$). We clearly see that, while in the case of the Hamiltonians $H_0$ and $H_1$ the energy of the ground state is unbounded from below in the limit $\kappa \to \infty$, the energy of the ground state of the total Hamiltonian $H_2$ is bounded as a consequence of the field “self-interacting” term $\lambda {\kappa }^2(a+a^{†}{)}^2$.Reuse & Permissions

Figure 2

The bipartite concurrence between two atoms in the ground state of the DM as a function of the scaled coupling parameter $\kappa /\omega$. We use the same notation as in Fig. 1. We can conclude that the interaction with the field mode induces a bipartite entanglement between atoms in the ground state of the Dicke model irrespective of the choice of the Hamiltonian.Reuse & Permissions