Bose-condensate tunneling dynamics: Momentum-shortened pendulum with damping

Bose-Einstein condensates in a double-well trap, as well ^3He-B baths connected by micropores, have been shown to exhibit Josephson-like tunneling phenomena. Unlike the superconductor Josephson junction of phase difference that maps onto a rigid pendulum of energy cos (), these systems map onto a momentum-shortened pendulum of energy -1-{p_^2}cos () and length 1-{p_^2}, where p_ is a population imbalance between the wells/baths. We study here the effect of damping on the four distinct modes of the nonrigid pendulum, characterized by distinct temporal mean values, 〈〉 and 〈p_〉. Damping is shown to produce different decay trajectories to the final equilibrium =0=p_ state that are characteristic dynamic signatures of the initial oscillation modes. In particular, damping causes -state oscillations with 〈〉= to increase in amplitude and pass through phase-slip states, before equilibrating. Similar behavior has been seen in ^3He-B experiments.