Entangling two Bose Einstein condensates in a double cavity system

We propose a scheme to transfer the quantum state of light fields to the collective density excitations of a Bose Einstein condensate (BEC) in a cavity. This scheme allows to entangle two BECs in a double cavity setup by transferring the quantum entanglement of two light fields produced from a nondegenerate parametric amplifier (NOPA) to the collective density excitations of the two BECs. An EPR state of the collective density excitations can be created by a judicious choice of the system parameters.