  In this Letter we study the entanglement of a quantum radiation field
interacting with a dielectric medium. In particular, we describe the quantum
mixed state of a field interacting with a dielectric through plasma and Drude
models and show that these generate very different entanglement behavior, as
manifested in the entanglement entropy of the field. We also present a formula
for a "Casimir" entanglement entropy, i.e., the distance dependence of the
field entropy. Finally, we study a toy model of the interaction between two
plates. In this model, the field entanglement entropy is divergent; however, as
in the Casimir effect, its distance-dependent part is finite, and the field
matter entanglement is reduced when the objects are far.
