Entanglement concentration for two atomic ensembles using an effective atom-light beamsplitter

We present a protocol for increasing the entanglement between two entangled atomic ensembles based on applying an approximate atom-light beamsplitter transformation to both ensembles. The effective asymmetric atom-light beamsplitter is created via a double-pass quantum non-demolition interaction between polarized light and a spin-polarized atomic ensemble, derived from the linearized dipole interaction. The entanglement concentration protocol itself uses the procrustean method, similar to that first devised for light by Browne et al (2003 Phys. Rev. A 67 062320), and includes photon counting after the interaction as the required non-Gaussian element. We calculate the output logarithmic negativity in this scheme and show that the entanglement between macroscopic ensembles can be increased with probabilities comparable with those for the light scheme even if on-off detectors of low efficiency are used.