Number fluctuation dynamics of atomic spin mixing inside a condensate.

We investigate the quantum dynamics of number fluctuations inside an atomic condensate during coherent spin mixing among internal states of the ground state hyperfine manifold, by quantizing the semiclassical nonrigid pendulum model in terms of the conjugate variable pair: the relative phase and the atom number. Our result provides a theoretical basis that resolves the resolution limit, or the effective "shot-noise" level, for counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.