Tunneling Dynamics of Bose-Einstein Condensates with Feshbach Resonances

We study tunneling dynamics of atomic pairs in Bose-Einstein condensates with Feshbach resonances. It is shown that the tunneling of the atomic pairs depends on not only the tunneling coupling between the atomic condensate and the molecular condensate, but also the inter-atomic nonlinear interactions and the initial number of atoms in these condensates. It is found that in addition to oscillating tunneling current between the atomic condensate and the molecular condensate, the nonlinear atomic-pair tunneling dynamics sustains a self-locked population imbalance: macroscopic quantum self-trapping effect. Influence of decoherence induced by non-condensate atoms on tunneling dynamics is investigated. It is shown that decoherence suppresses atomic-pair tunneling.Comment: 6 pages, 2 figures, RevTex, to appear in Phys. Rev. A (July 2000

Frames and operators in Schatten classes

Let $T$ be a compact operator on a separable Hilbert space $H$. We show that, for $2\le p<\infty$, $T$ belongs to the Schatten class $S_p$ if and only if $\{\|Tf_n\|\}\in \ell^p$ for \emph{every} frame $\{f_n\}$ in $H$; and for $0<p\le2$, $T$ belongs to $S_p$ if and only if $\{\|Tf_n\|\}\in\ell^p$ for \emph{some} frame $\{f_n\}$ in $H$. Similar conditions are also obtained in terms of the sequence $\{\}$ and the double-indexed sequence $\{\}$.Comment: 27 page