Split spin-squeezed Bose-Einstein condensates

We investigate and model a method for producing entanglement between two spatially separated Bose-Einstein condensates (BECs). In our approach, a spin-polarized BEC is squeezed using a (S-z)(2) interaction, then are split into two separate clouds. After the split, we consider that the particle number in each cloud collapses to a fixed number. We show that this procedure is equivalent to applying an interaction corresponding to squeezing each cloud individually plus an entangling operation. We analyze the system`s inter-well entanglement properties and show that it can be detected using correlation-based entanglement criteria. The nature of the states is illustrated by Wigner functions and have the form of a correlated squeezed state. The conditional Wigner function shows high degrees of non-classicality for dimensionless squeezing times beyond 1/root N, where N is the number of particles per BEC.