Nonlocality under Jaynes-Cummings evolution: Beyond pseudospin operators

We revisit the generation and evolution of Bell nonlocality in hybrid scenarios of which the dynamics is determined by the Jaynes-Cummings Hamiltonian, a relevant example of which is the atom-cavity system. Previous approaches evaluate the nonlocality through the well-known qubit-qubit Clauser-Horne-Shimony-Holt (CHSH) formulas, using combinations of pseudospin operators for the electromagnetic (EM) field observables. While such an approach is sensible, it is far from optimal. In the present work we have used recent results on optimal Bell violation in qubit-qudit systems, showing that the nonlocality is much greater than previously estimated, both with and without noise. In addition, we provide an optimal treatment of noise, ensuring that our results are the best possible within this framework. We illustrate the results using different initial states for the EM field, including squeezed and coherent states. In addition, we study the asymptotic behavior of the entanglement. Remarkably, starting with a generic separable pure coherent state, the asymptotic mixed state is entangled, though it does not violate CHSH inequalities.