Collective Excitations in Double Quantum Dots

We analyse the ground state properties of vertical double quantum dots in the lowest Landau level regime for filling factor \nu=2. This analysis follow two lines: on the one hand, we study the dispersion relation of different collective excitations and look for the roton-type minima that signal some type of order within the ground state. On the other hand, we calculate expected values of the antiferremagnetic order operator defined as <S_x^RS_x^L>. We conclude that of the three existing types of ground state at \nu=2 the canted and symmetric states show spin order on the plane of the dots. In the case of the canted state, two types of spin order are shown as a consequence of the coupling between spin and isospin. We propose that one of the excitations obtained over the symmetric state could be the origin of one of the decoherent processes detected experimentally in qubit sysytems.