Entanglement and non-Markovianity of quantum evolutions

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A very simple example is a qubit interacting via the Hamiltonian H = | 01 ⟩ ​ ⟨ 10 | + | 10 ⟩ ​ ⟨ 01 | H=|01\rangle\langle 10|+|10\rangle\langle 01| with another qubit playing the role of the environment, i.e. the time evolution will swap back and forth with the evironmental qubit. Evidently this will periodically increase and decrease the entanglement between an ancillary qubit and the system

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A similar result can be obtained for spontaneous emission and by using the Lorentzian spectral density for the Jaynes-Cummings model we would obtain a behaviour in total agreement with the results in Fig. 2 in [ 6 ]

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