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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 be a compact operator on a separable Hilbert space . We show that,
for , belongs to the Schatten class if and only if
for \emph{every} frame in ; and for
, belongs to if and only if for
\emph{some} frame in . Similar conditions are also obtained in
terms of the sequence and the double-indexed sequence
.Comment: 27 page
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