Double-occupancy probability and entanglement of two holes in double Ge/Si quantum dots

We have calculated the exchange energy, double occupation probability of the lowest singlet state, and degree of entanglement of two holes in vertically coupled double Ge/Si quantum dots. We determined the conditions on which the exchange coupling is large enough for a fast swap operation in quantum computation and the double-occupancy probability is still low, thus maximizing the entanglement for a small computation error. We found that both the degree of entanglement and double-occupancy probability for quantum dots with different dot size collapse onto universal, size independent curves when plotted as a function of singlet-triplet splitting.