where x ′ k = x -x k with k = 1 for x < 0 (left) and k = 2 for x > 0 (right), and the h k 's control the relative depth of the two wells, with the detuning dened as ε = h 2 -h 1 . y denotes the coordinate perpendicular to the interdot axis (x). A notable property of V TCO is the fact that it allows for the formation of a smooth interwell barrier between the individual wells whose height V b can be varied independently from the interdot distance d = x 2 -x 1 ; see Fig. for an illustration. The most general shapes described by V TCO are two semiellipses connected by the smooth neck, V neck (x). x 1 < 0 and x 2 > 0 are the centers of these semiellipses. In this paper, we take