Charge occupancy of two interacting electrons on artificial molecules: Exact results

We present exact solutions for two interacting electrons on an artificial a tom and on an artificial molecule made by one and two (single level) quantu m dots connected by ideal leads. Specifically, we calculate the accumulated charge on the dots as function of the gate voltage epsilon (0), for variou s strengths of the electron-electron interaction U and of the hybridization between the dots and the (one-dimensional) leads gamma. For gamma <1 and 2 (<gamma>-1) drop epsilon (00) < <epsilon>(0) < 0 there are no bound states. As <epsilon>(0) decreases beyond epsilon (00), the accumulated charge P in the two-electron ground state increases in gradual steps from 0 to 1 and t hen to 2. The values P similar toO represent an "insulating" state, where b oth electrons are bound to shallow states on the impurities. The value of P approximate to1 corresponds to a "metal," with one electron localized on t he dots and the other extended on the leads. The value of 2 corresponds to another "insulator," with both electrons strongly localized. The width Of t he "metallic" regime diverges with U for the single dot, but remains very n arrow for the double dot. These results are contrasted with the simple Coul omb blockade picture.