Bogoliubov theory of entanglement in a Bose-Einstein condensate

We consider a Bose-Einstein condensate that 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 analyzed in detail by developing a Bogoliubov theory that 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 predicts 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.