(color online) (a) Schematic diagram of the superexchange and inter-orbital spin-exchange interactions. The
atoms are independently trapped in the shallow (deep) superlattice, whose nuclear spin states are marked by
and
. The superexchange process (green arrow) happens between AFM states (
) via virtual tunneling (black dashed arrows), while two-orbital spin-exchange interaction (red arrows) couples
with the magnetic state
. (b) Time evolution of the spin imbalance Ngz of the g atoms (black) and the population of the state
(blue) for a small magnetic field (the resulting differential Zeeman shift can be ignored) and the initial state
. The envelope of Ngz is given by
(red). The collapse and revival happen at
and
, respectively. (c) Energy levels of the perturbation model (left) and the eigenstates (right).
.
are the coupling matrix elements. δ is the energy shift. The red solid and blue dashed arrows indicate the near-resonant coupling and far-off-resonant coupling, respectively. (d) Time evolution of the spin-imbalance of g atoms with
(black line). The envelope (red solid) corresponds to
. The parameters are
,
,
in panels (b) and (d).
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