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Entanglement control via reservoir engineering in ultracold atomic gases

We study the entanglement of two impurity qubits immersed in a Bose-Einstein condensate (BEC) reservoir. This open quantum system is particularly interesting because the reservoir and system parameters are easily controllable and the reduced dynamics is highly non-Markovian. We show how the model allows for interpolation between a common dephasing scenario and an independent dephasing scenario by simply modifying the wavelength of the superlattice superposed to the BEC, and how this influences the dynamical properties of the impurities. We demonstrate the existence of very rich entanglement dynamics correspondent to different values of reservoir parameters, including phenomena such as entanglement trapping, entanglement sudden death, revivals of entanglement, and BEC-mediated entanglement generation. In the spirit of reservoir engineering, we present the optimal BEC parameters for entanglement generation and trapping, showing the key role of the ultracold gas interactions.