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Entanglement is essential in quantum information science. Typically, theinevitable coupling between quantum systems and environment inhibitsentanglement from being created between long-distance subsystems and beingmaintained for a long time. In this paper, we show that when the environment iscomposed of a bath of massive scalar fields, the region of the separationwithin which entanglement can be generated is significantly enlarged, and thedecay rate of entanglement is significantly slowed down compared with those inthe massless case, when the mass of the field $m$ is smaller than but close tothe transition frequency of the qubits $\omega$. When $m\geq\omega$, theinitial entanglement can be maintained for an arbitrarily long time, regardlessof the environmental temperature. Therefore, in principle, it is possible toachieve long-distance entanglement generation and long-lived entanglement bymanipulating the energy level spacing of the two-level systems with respect tothe mass of the field.

Entanglement dynamics for two-level quantum systems coupled with massive scalar fields