Quantum nondemolition measurement based generation of entangled states in two Bose-Einstein condensates

We theoretically study a scheme for generating entanglement between two Bose-Einstein condensates (BECs). The scheme involves placing two BECs in the path of a Mach-Zehnder interferometer, where the coherent light interacts with the atoms due to a quantum nondemolition Hamiltonian. In contrast to standard approaches where a Holstein-Primakoff approximation is used, we use an exact wavefunction approach where the atoms can be initialized in an arbitrary state and the light-atom interaction times can be arbitrary. In the short time regime, it is possible to construct a very simple approximate theory for the overall effect of the scheme: amplitudes in the superposition between the two BECs with unequal spin eigenvalues are damped. We analyze the types of correlations, entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell correlations that are produced and show that the state is similar to a spin-EPR state. Using a two-pulse sequence the correlations can be dramatically improved, where the state further approaches a spin-EPR state.