Wave-function recombination instability in cold-atom interferometers

Cold-atom interferometers use guiding potentials that split the wave function of the Bose-Einstein condensate and then recombine it. We present a theoretical analysis of the wave-function recombination instability that is due to the weak nonlinearity of the condensate. It is most pronounced when the accumulated phase difference between the arms of the interferometer is close to an odd multiple of $\pi$ and consists in exponential amplification of the weak ground state mode by the strong first excited mode. The instability exists for both trapped-atom and beam interferometers.