Entanglement properties in the inhomogeneous Tavis-Cummings model

We study the properties of atomic entanglement in the eigenstates spectrum of the inhomogeneous Tavis-Cummings model. The inhomogeneity is present in the coupling among the atoms with quantum electromagnetic field. We calculate analytical expressions for the concurrence, and we find that this exhibits a strong dependence on the inhomogeneity.

Figure 1

Levels scheme that involve the Hilbert space. Here is possible to see the Hilbert-space growth due to the inhomogeneous coupling.

Figure 2

Contribution (%) of second row of Fig. 1 to the energy as a function of the number of atoms $N$. $\Delta E^{\left(k\right)}=100\left(\mid (E_1^{\left(k\right)}-E_2^{\left(k\right)})∕E_1^{\left(k\right)}\mid \right)$, where $E_{1,2}^{\left(k\right)}$ are the energies for $k$ excitations using one or two rows of Fig. 1.

Figure 3

Bipartite concurrence $C_{1,j}$ between the first and $j\text{th}$ atoms for $k=1$ excitation for different number of atoms, $N$.

Figure 4

Bipartite concurrence $C_{1N}$ between the first and last atoms for $k=1,2,\dots ,6$ excitations as a function of the number of atoms $N$.

Figure 5

Bipartite concurrence $C_{1,j}$ between the first and $j\text{th}$ atoms for $k=1,2,\dots ,6$ excitations with $N=20$ atoms.