Selective Spin Coupling through a Single Exciton

We present a novel scheme for performing a conditional phase gate between two spin qubits in adjacent semiconductor quantum dots through delocalized single exciton states, formed through the interdot Förster interaction. We consider two resonant quantum dots, each containing a single excess conduction band electron whose spin embodies the qubit. We demonstrate that both the two-qubit gate and arbitrary single-qubit rotations may be realized to a high fidelity with current semiconductor and laser technology.

Figure 1

Schematic of the energy level structure of two resonantly coupled QDs, showing its dependence on the spin state of the excess electron on each dot. When the spins are both in state $|1\rangle$ an energy shift of the single exciton states occurs due to their Förster coupling. Hence a phase shift may be accumulated using a laser resonant with the dipole allowed transition. This does not occur for any of the other states shown due to the Pauli blocking mechanism.

Figure 2

Phase (top) and amplitude (bottom) of states $|10\rangle$ and $|11\rangle$ during the CPHASE gate operation, with $V_F=0.85\mathrm{m}\mathrm{e}\mathrm{V}$, $V_{XX}=5\mathrm{m}\mathrm{e}\mathrm{V}$, and ${\omega }_a=2\mathrm{e}\mathrm{V}$.

Figure 3

Population of the state of a single qubit during the proposed $X$-rotation gate induced by a two-laser Raman transition. Various values of the exciton decay rate $\gamma$ and laser detuning $\nu$ are shown with ${\omega }_a=2\mathrm{e}\mathrm{V}$, and $\Omega =1.33\mathrm{m}\mathrm{e}\mathrm{V}$ for both lasers.