  We propose a protocol by which entanglement can be extracted repeatedly from
a quantum field. In analogy with prior work on entanglement harvesting, we call
this protocol entanglement farming. It consists of successively sending pairs
of unentangled particles through an optical cavity. Using non-perturbative
Gaussian methods, we show that in certain generic circumstances this protocol
drives the cavity field towards a non-thermal metastable state. This state of
the cavity is such that successive pairs of unentangled particles sent through
the cavity will reliably emerge significantly entangled. We calculate
thermodynamic aspects of the harvesting process, such as energies and
entropies, and also the long-term behavior beyond the few-mode approximation.
Significant for possible experimental realizations is the fact that this
entangling fixed point state of the cavity is 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.
