Bound entanglement in the Jaynes-Cummings model

TL;DR

This paper investigates the entanglement properties in the Jaynes-Cummings model, revealing the existence of bound entangled states and demonstrating that the interaction can generate such entanglement between a qubit and a mode.

Contribution

It is the first to show bound entangled states in the Jaynes-Cummings model and that the interaction can produce bound entanglement.

Findings

Bound entangled states exist for N>3 in the model.

The Jaynes-Cummings interaction can generate bound entanglement.

States commuting with the conserved number operator are key to analysis.

Abstract

We study in detail entanglement properties of the Jaynes-Cummings model assuming a two-level atom (qubit) interacting with the first $N$ levels of an electromagnetic field mode (qudit) in a cavity. In the Jaynes-Cummings model, the number operator is the conserved quantity that allows for the exact diagonalization of the Hamiltonian and thus we study states that commute with this conserved quantity and whose structure is preserved under the Jaynes-Cummings dynamics. Contrary to the common belief, we show that there are bound entangled states that satisfy the symmetries imposed by the conservation of the number of excitations when $N>3$. Furthermore we show that \emph{the Jaynes-Cummings interaction can be used to generate bound-entanglement} between the atom and the mode.