Entanglement between a ΛΛ-type three-level atom and its spontaneous emission fields

The entanglement between a ΛΛ-type three-levels atom and its spontaneous emission field is studied by using the quantum entropy. The results show that, there is a steady state entanglement between the ΛΛ-type three-level atom and its spontaneous emission field. The entanglement between the ΛΛ-type three-level atom and its spontaneous emission fields decreases due to the coherent superposition of the atomic levels. The spontaneous emission process of the atom is one of the atom is entangled with its spontaneous emission fields. For the two fields related to the two transition in the ΛΛ-type three-level atom, we have shown that they are classically correlated, but there is no quantum entanglement between the two fields.