Phase resolution for Bose-Einstein condensates

We discuss how the nature of the relative phase between two entangled condensates differs depending on whether the entanglement is established by measurements or by coupling. In the former case, the limit of the resulting phase resolution scales inversely with the square root of the number of atoms. This limit can be surpassed, however, when the condensates are entangled by coupling and can reach the fundamental Heisenberg limit where the phase resolution scales inversely with the number of atoms involved.