Entanglement production in the decay of a metastable state

When a metastable state decays into radiation, there must be entanglement between the radiation and the decaying system, as well as between radiation collected at late and early times. We study the interplay between these two types of entanglement in simple Gaussian models in the Markov approximation. We define, via a windowed Fourier transform, multimode quantum states associated with radiation fragments produced at different times and compute the corresponding entanglement entropy increments. On the basis of these results, we argue that such entropy increments are useful entanglement measures, especially in cases, such as Hawking radiation, where one wishes to separate the radiation into ``old'' and ``new.''