We consider a system of three weakly coupled Bose-Einstein condensates and
two atomic quantum dots embedded in the barriers between the condensates. Each
dot is coupled to two neighboring condensates by optical transitions and can be
described as a two-state system, or a pseudospin 1/2. Although there is no
direct coupling between the dots, an effective interaction between the
pseudospins is induced due to their coupling to the condensate reservoirs. We
investigate this effective interaction, depending on the strengths of the
dot-condensate coupling T and the direct coupling J between the condensates. In
particular, we show that an initially ferromagnetic arrangement of the two
pseudospins stays intact even for large T/J. However, antiferromagnetically
aligned spins undergo peculiar "breathing" modes for weak coupling T/J<1, while
for strong coupling the behaviour of the spins becomes uncorrelated.Comment: 5 pages, 7 figure
