  In this paper, we present a method to generate continuous-variable-type
entangled states between photons and atoms in atomic Bose-Einstein condensate
(BEC). The proposed method involves an atomic BEC with three internal states, a
weak quantized probe laser and a strong classical coupling laser, which form a
three-level Lambda-shaped BEC system. We consider a situation where the BEC is
in electromagnetically induced transparency (EIT) with the coupling laser being
much stronger than the probe laser. In this case, the upper and intermediate
levels are unpopulated, so that their adiabatic elimination enables an
effective two-mode model involving only the atomic field at the lowest internal
level and the quantized probe laser field. Atom-photon quantum entanglement is
created through laser-atom and inter-atomic interactions, and two-photon
detuning. We show how to generate atom-photon entangled coherent states and
entangled states between photon (atom) coherent states and atom-(photon-)
macroscopic quantum superposition (MQS) states, and between photon-MQS and
atom-MQS states.

Quantum Physics