Coherent population trapping in negatively charged self-assembled quantum dots using a train of femtosecond pulses

We demonstrate the coherent population trapping in a single quantum dot and an ensemble of negatively charged quantum dots using a train of femtosecond pulses. Particularly in an ensemble of quantum dots, we show that the detrimental effects due to the inhomogeneous distribution of their properties can be minimized by appropriately choosing the pulse-train parameters and the magnetic-field strength in such a way that the electron-Zeeman splitting is an integer multiple of the pulse repetition rate.

Figure 1

Four-level model of a negatively charged quantum dot.

Figure 2

Accumulation of coherence in the single QD as a function of the irradiated number of pulses for the different values of pulse intervals.

Figure 3

(a) Accumulation of coherence in the single QD for the different values of pulse area and (b) the corresponding evolution of coherence as a function of pulse repetition rate. (c) Accumulation of coherence in an ensemble of QDs for the different values of pulse area and (d) the corresponding evolution of dark state populations as a function of the irradiated number of pulses.

Figure 4

Variation in the dark state population in the single QD as a function of the value of dipole moments with ${\overline{\mu }}_x=8\mathrm{D}$, $T_R=5\mathrm{ns}$, and $E_0=1.62\times {10}^5\mathrm{V}/\mathrm{cm}$. The number of irradiated pulses are $N=50$ (dot-dashed line), 100 (solid line), and 200 (dashed line), respectively. The solid line at the center represents the distribution function $f\left(\mu \right)$.

Figure 5

Variation in the dark state population in the single QD as a function of electron-spin $g$ factors with $\overline{g_x^e}=0.57$, $T_R=5\mathrm{ns}$, and $\Theta =\pi /5$. The employed magnetic-field strengths are $B_x=250.70$ (dot-dashed line), 125.35 (solid line), and 25.07 mT (dashed line), respectively. The solid line at the center represents the distribution function $f\left(g\right)$. The number of irradiated pulses is $N=200$.