Entanglement and errors in the control of spins by optical coupling

We analyze the optical quantum control of impurity spins in proximity to a quantum dot. A laser pulse creates an exciton in the dot and controls the spins by indirect coupling. We show how to determine the control parameters using as an illustration the production of maximal spin entanglement. We consider errors in the quantum control due to the exciton radiative recombination. The control errors in the adiabatic and nonadiabatic case are compared to the threshold needed for scalable quantum computing.

Figure 1

(Color online) Scheme the system: localized spins located near self-assembled QDs are coupled by an exciton created by a laser pulse. Dots of different size provide selective control and readout.

Figure 2

(Color online) Energy level diagram and optical selection rules for ${\sigma }_{+}$-polarized light. In $n=1$, the total splitting is $j=6V$.

Figure 3

(Color online) Nonadiabatic control, $\gamma =0$. Evolution of the $\mid S⟩$ [solid (blue) line] and $\mid T_0⟩$ [dashed (red) line] populations under a Gaussian pulse of area $8\pi$. The temporal width of the pulse $\tau$ is $7.02\mathrm{ps}$ and the ratio $\Omega ∕V$ is 0.6697. (Inset) Real [dashed (green) line] and imaginary [solid (red) line] part of the coherence $⟨S\mid \rho \mid T_0⟩$.

Figure 4

(Color online) Adiabatic control, $\gamma =0$. The laser is tuned to $2\mathrm{meV}$ below the bare excitonic energy. Evolution of the $\mid S⟩$ [solid (blue) line] and $\mid T_0⟩$ [dashed (red) line] populations under a Gaussian pulse. The temporal width of the pulse $\tau$ is $10.2\mathrm{ps}$ and the ratio $\Omega ∕V$ is 1.24. (Inset) Real [dashed (green) line] and imaginary [solid (red) line] part of the coherence $⟨S\mid \rho \mid T_0⟩$.

Figure 5

(Color online) Log-log plot of the deviation from maximal entanglement (upper panel) and maximal purity (lower panel) as a function of the radiative recombination $\gamma$ (in meV). Solid (blue) line, adiabatic evolution. Dashed (red) line, nonadiabatic evolution.