Figure 12.1: (a) Schematic of a quantum dot embedded in a host. The electron wavefunction is largely confined to the dot material, but does penetrate into the host (barrier) material. (b) Through the application of an electric field the wavefunction of the dot state is altered, including its amplitude in the barrier region. This produces an electric-field dependence of the g-factor, which can be used to rotate the electron spin relative to the spin in other dots.

Figure 12.2: The wavefunctions in the individual dots (dark grey) do not overlap significantly most of the time. Under the application of an electric field the wavefunctions (black) leak more into the barrier region and overlap. This leads to a spin- spin interaction between the dots, which provides a controllable [J(t)] Heisenberg Hamiltonian.

Figure 12.3: (a) Phosphorus atom embedded in a silicon host. The extra electron the phosphorus atom carries is bound to it in a highly extended state (~10 nm diameter). (b) An electric field can be used to modify the overlap of this electron with the phosphorus nucleus, changing the resonant frequency of its nuclear spin.

Figure 12.4: The wavefunctions of the individual bound electrons (dark grey) do not overlap significantly most of the time. Under the application of an electric field the wavefunctions (black) overlap more with each other. This leads to a spin-spin interaction between the electronic states, which is communicated to the nuclei through the hyperfine and produces a controllable Heisenberg interaction between the nuclear spins.