Electrical Measurement of a Two-Electron Spin State in a Double Quantum Dot

We propose a scheme for electrical measurement of two-electron spin states in a semiconductor double quantum dot. We calculated the adiabatic charge transfer when surface gates are modulated in time. Because of spin-orbit coupling in the semiconductor, spatial displacement of the electrons causes a total spin rotation. It follows that the expectation value of the transferred charge reflects the relative phase as well as the total spin population of a prepared singlet-triplet superposition state. The precise detection of the charge transfer serves to identify the quantum superposition.

Figure 1

(a) Bloch sphere of the $S\mathrm{\text{−}}{T}_0$ spin subspace. The angle $\theta$ characterizes the total spin populations, whereas the angle $\varphi$ denotes the relative phase. (b) Scattering processes in the DQD; $|S⟩$ and $|T_0⟩$ couple with each other through the doubly occupied states. $|S_{g(e)}⟩$ is a linear combination of $|(2,0)S⟩$ and $|(0,2)S⟩$, which diagonalizes the doubly occupied states when we set $T=P=0$ virtually.

Figure 2

Sequence of gate voltage manipulations under consideration. The upper panel shows the potential bias between the left and the right dots. The overlap of the orbitals in the two dots $\Gamma$ is moved up and down by the gate-controlled potential barrier.