  The ability to deterministically generate genuine multi-partite entanglement
is fundamental for the advancement of quantum information science. We show that
the interaction between entangled twin beams of light and an atomic ensemble
under conditions for electromagnetically induced transparency leads to the
generation of genuine hybrid tri-partite entanglement between the two input
fields and the atomic ensemble. In such a configuration, the system is driven
through dissipation to a steady state given by the hybrid entangled state. To
show the presence of the genuine hybrid entanglement, we introduce a new
approach to treat the atomic operators that makes it possible to show a
violation of a tri-partite entanglement criterion based on the properties of
the two optical fields and collective properties of the atomic ensemble.
Additionally, we show that while each of the input optical fields does not
exhibit single beam quadrature squeezing, as the fields propagate through the
atomic medium their individual quadratures can become squeezed and in some
cases oscillate between the presence and absence of squeezing. Finally, we
propose a technique to characterize the tri-partite entanglement through joint
measurements of the fields leaving the atomic medium, making such an approach
experimentally accessible.
