In this article, we study thermal entanglement between two-coupled two-level atoms interacting with a single-mode cavity field. The cavity mode is assumed to be initially in the vacuum state and the detuning parameter is large. The thermal entanglement in this two-qubit system is quantified in terms of the concurrence, as a proper measure for two-qubit mixed states. We investigate how the thermal entanglement depends on temperature, dipole coupling between the atoms and detuning parameter. In addition, we shall use the generated thermally atomic entangled state as a quantum channel for teleportation and we mainly concentrate on the fidelity of teleportation. Finally, the relationship between the quantum coherence and entanglement will be discussed.

Deformed Jaynes–Cummings model (JCM) has a physical importance in quantum optics. Hence, we investigated the nonlinear JCM including the intensity-dependent coupling constant and the additional Kerr term. The cavity was assumed to be in thermal equilibrium with a heat reservoir at temperature T . Using the generators of a closed algebra which reduces to the su(1, 1) and Heisenberg–Weyl algebras at limiting cases, and considering the total excitation number as a constant of motion, the total Hilbert space decomposes into two subspaces. So the eigenvalues and the corresponding eigenvectors were obtained. We derived the thermal density matrix and analysed the fidelity and thermal entanglement using negativity measure. Furthermore, we studied the Berry phase of the nonlinear atom–field system and explored the influence of nonlinearity on the quantum phase transition (QPT) point and entanglement. It is found that the deformation parameter can strongly affect the fidelity, negativity and QPT point.