Entanglement generation and Hamiltonian simulation in   Continuous-Variable Systems
  Several recent experiments have demonstrated the promise of atomic ensembles for quantum teleportation and quantum memory. In these cases the collective internal state of the atoms is well described by continuous variables $X_1, P_1$ and the interaction with the optical field ($X_2, P_2$) by a quadratic Hamiltonian $X_1X_2$. We show how this interaction can be used optimally to create entanglement and squeezing. We derive conditions for the efficient simulation of quadratic Hamiltonians and the engineering of all Gaussian operations and states. 
Barbara Kraus, Klemens Hammerer, Geza Giedke, and J. Ignacio Cirac