Entanglement farming: Harnessing the properties of fixed points in quantum evolution

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We show that in certain generic circumstances the state of light of an optical cavity traversed by beams of atoms is naturally driven towards a non-thermal metastable state. This state can be such that successive pairs of unentangled particles sent through the cavity will reliably emerge significantly entangled thus providing a renewable source of quantum entanglement. Significant for possible experimental realizations is the fact that this entangling fixed point state of the cavity can be reached largely independently of the initial state in which the cavity was prepared. Our results suggest that reliable entanglement farming on the basis of such a fixed point state should be possible also in various other experimental settings, namely with the to-be-entangled particles replaced by arbitrary qudits and with the cavity replaced by a suitable reservoir system.