Accuracy of Circular Polarization as a Measure of Spin Polarization in Quantum Dot Qubits

A quantum dot spin light emitting diode provides a test of carrier spin injection into a qubit and a means for analyzing carrier spin injection and local spin polarization. Even with 100% spin-polarized carriers the emitted light may be only partially circularly polarized due to the geometry of the dot. We have calculated carrier polarization-dependent optical matrix elements for $\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ self-assembled quantum dots (SAQDs) for electron and hole spin injection into a range of quantum dot sizes and shapes, and for arbitrary emission directions. Calculations for typical SAQD geometries with emission along $[110]$ show light that is only 5% circularly polarized for spin states that are 100% polarized along $[110]$. Measuring along the growth direction gives near unity conversion of spin to photon polarization and is the least sensitive to uncertainties in SAQD geometry.

Figure 1

(a) The quantum dot geometry. (b) Electron and hole wave functions for a dot with $e=1.4$ and $h=2.8\mathrm{n}\mathrm{m}$.

Figure 2

(a) Polarization along $[110]$, as a function of elongation. (b) Polarization along $[110]$, as a function of band gap.

Figure 3

Polarization as a function of spin polarization and light emission direction for a SAQD with $h=2.8\mathrm{n}\mathrm{m}$, $e=1.4$, and $E_g=1.36\mathrm{e}\mathrm{V}$. The SAQD geometry was chosen to make the features more visible. (a) Surface showing $P_d\widehat{d}=\widehat{d}(I_d^{+}-I_d^{-})/(I_d^{+}+I_d^{-})$. (b) $P_d\widehat{d}$ in the $(110)$ and $(1\overline{1}0)$ planes. (c) $P_d\widehat{d}$ in the $(001)$ plane.