Ultrafast optical control of electron spin coherence in charged $\mathrm{GaAs}$ quantum dots

Impulsive stimulated Raman excitation with coherent optical fields is used for controlling the electron spin coherence in a charged $\mathrm{GaAs}$ quantum dot ensemble through an intermediate charged exciton (trion) state. The interference between two stimulated Raman two-photon quantum mechanical pathways leading to the spin coherence allows us to control the electron spin coherence on the time scale of the Larmor precession frequency. We also demonstrate, both theoretically and experimentally, that ultrafast manipulation of the spin coherence is possible on the time scale of the optical laser frequency, and analyze the limitations due to the trion and spin decoherence times.

Figure 1

(Color online) (a) Excitation picture for the charged QD, with ground states $\mid g=0,1⟩$ denoting electron spin projections $\mid \pm \frac{1}{2}⟩$ along the $x$-axis symmetrically split by $\hslash {\omega }_L={\mu }_B{g}_{e,x}{B}_x$, where ${\mu }_B$ is the Bohr magneton. The degenerate trion states $\mid t\pm ⟩$ are labeled by the heavy-hole angular momentum projection $\mid \pm \frac{3}{2}⟩$ along the growth ($z)$ axis, with transition energy $\hslash ({\omega }_g\pm \frac{{\omega }_L}{2})$. Solid (gray) lines denote transitions excited by ${\sigma }^{+}\left({\sigma }^{-}\right)$ light. (b) Schematic diagram of the experimental setup. (c) Double-sided Feynman diagrams for different quantum-mechanical pathways due to SR2Ps leading to creation of spin coherence. $\mid T⟩$ is used to denote either trion state $\mid t\pm ⟩$. There is a corresponding set of diagrams (not shown) starting from the density operator $\mid 1⟩⟨1\mid$.

Figure 2

(Color online) Coherent optical manipulation of electron spin coherence in charged quantum dots. The data shown is the DT signal as a function of $({\tau }_x,{\tau }_y)$, with the magnetic field $B_x=2.2\mathrm{T}$. The peaks show the arrival of the primary and control pulses. The spin coherence is read out by the probe, with the probe delay scanned along the ${\tau }_x$-axis, while the ${\tau }_y$-axis denotes the delay between the control and primary pulses. Inset shows the temporal sequence of laser pulses for coherent optical control of the spin coherence. The arrows represent the position where the delay of the corresponding laser pulse is parked for the experiments of Fig. 3.

Figure 3

(Color online) (a) DT spectrum (no control pulse) with the pump-probe delay fixed at $+10\mathrm{ps}$. The shaded region is the pulse spectrum with the pump spectral position, fixed for all the other experiments denoted by the red arrow, and $T$ $\left(X\right)$ labels the trion (exciton) resonances. (b), (c) Horizontal slice from Fig. 2 at ${\tau }_y=120$, $240\mathrm{ps}$, respectively, with dashed lines representing data, and solid lines representing fits to the data using Eq. (2). In (c) dotted lines represent the fit to the single pump pulse data. The shaded area represents the difference in signals obtained with and without the control pulse. (d) Vertical slice (solid circles) from Fig. 2 at ${\tau }_x=620\mathrm{ps}$. Open circles are data from a classical first-order auto-correlation between the primary and control fields.

Figure 4

(Color online) Femtosecond coherent optical control of spin coherence enabled through Feynman diagram III. Solid symbols denote data obtained by fixing the coarse delay ${\tau }_y$, and scanning the fine delay ${\tau }_p$. In theoretical calculations, the optical pulses are assumed Gaussian with the intensity given by $I\left(\omega \right)=\exp (-\frac{4\ln 2{\omega }^2}{\delta {\omega }^2})$ $(\hslash \delta \omega =0.35\mathrm{meV})$, as measured by the classical interferogram.