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

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