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

Abstract

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 f that maps onto a rigid pendulum of energy cos(Φ), these systems map onto a momentum-shortened pendulum of energy -√ 1-p_Φ²cos(Φ) and length -√ 1-p_Φ², where pΦ 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, <Φ> and <p_Φ>. Damping is shown to produce different decay trajectories to the final equilibrium Φ=0=p_Φ state that are characteristic dynamic signatures of the initial oscillation modes. In particular, damping causes π-state oscillations with <Φ>=π to increase in amplitude and pass through phase-slip states, before equilibrating. Similar behavior has been seen in ³He-B experiments.