Single-shot initialization of electron spin in a quantum dot using a short optical pulse

We propose a technique to initialize an electron spin in a semiconductor quantum dot with a single short optical pulse. It relies on the fast depletion of the initial spin state followed by a preferential, Purcell-accelerated deexcitation toward the desired state thanks to a micropillar cavity. We theoretically discuss the limits on initialization rate and fidelity and derive the pulse area for optimal initialization. We show that spin initialization is possible using a single optical pulse down to a few tens of picoseconds wide.

Figure 1

(a) QD-micropillar device in Voigt geometry. (b) Four-level system and corresponding optical transitions (solid line, $X$ polarized; dashed line, $Y$ polarized), with $\Omega$ and $\Gamma$ the pumping and relaxation rates, respectively. (c) Initialization time $T_0$ for $F_p=0$, 10, and 30 as a function of $\Omega /\Gamma$.

Figure 2

(a) Population of $|e^{-}\rangle$ as a function of time, numerically integrated for $F_p=30$ and $B=6\hspace{0.5em}T$, using different pumping rates around the optimal value ${\Omega }_{\mathrm{opt}}=(F_p+1)\Gamma /2$. (b) Final initialization error as a function of the magnetic field, for $F_p=30$, 40, and $50$, for the optimal pumping rate.

Figure 3

(a) Pulse area for optimal initialization for $F_p=30$, $40$, and $50$, as a function of the square pulse duration, as deduced from Eq. (7). (b) Initialization error corresponding to this pulse area, for $B=6$ and 10 T, and in the limit of infinite magnetic field, with a Purcell factor $F_p=40$.

Figure 4

(a) Optical-pulse normalized intensity and corresponding populations of $|e^{+}\rangle$ and $|e^{-}\rangle$ states, as a function of time (40 ps FWHM Gaussian pulse, with $F_p=40$ and $B=6$ T). (b) Initialization error as a function of the Gaussian pulse width for $6$ T, $10$ T, and infinite magnetic fields, with $F_p=40$. Inset: Required pulse area for optimal initialization using a Gaussian pulse, for $F_p=30$, $40$, and $50$.