Coherent quantum tunneling between two Bose-Einstein condensates

We study an elementary model of two tunneling Bose-Einstein condensates with an atom detector in one of the traps. Stochastic simulations of atom detection in one trap show an oscillation of atom number between traps even though the condensates are initially in equal number Fock states. The oscillation has a random amplitude depending on the phase difference between the condensates, which coincides with that given by a spontaneously broken symmetry argument.