Bogoliubov theory of entanglement in a Bose-Einstein condensate

We consider a Bose-Einstein condensate which is illuminated by a short resonant light pulse that coherently couples two internal states of the atoms. We show that the subsequent time evolution prepares the atoms in an interesting entangled state called a spin squeezed state. This evolution is analysed in detail by developing a Bogoliubov theory which describes the entanglement of the atoms. Our calculation is a consistent expansion in $1/\sqrt{N}$, where $N$ is the number of particles in the condensate, and our theory predict that it is possible to produce spin squeezing by at least a factor of $1/\sqrt{N}$. Within the Bogoliubov approximation this result is independent of temperature.