Beating of Exciton-Dressed States in a Single Semiconductor $\mathrm{InGaAs}/\mathrm{GaAs}$ Quantum Dot

We report picosecond control of excitonic dressed states in a single semiconductor quantum dot. A strong laser pulse couples the exciton and biexciton states, to form an Autler-Townes doublet of the neutral exciton transition. The Rabi-splitting, and hence the admixture of the dressed states follows the envelope of the picosecond control laser. We create a superposition of dressed states, and observe the resulting beat: a direct measurement of a Rabi oscillation in time delay rather than the usual power domain.

Figure 1

Energy-level diagram of a neutral dot. (a) There are four excitonic states: empty $|0⟩$, exciton spin up and spin down $\mid \uparrow ⟩$, $\mid \downarrow ⟩$, and the biexciton $|2X⟩$. (${\omega }_c$) The control laser couples the $\uparrow \mathrm{\text{−}}2X$ states, while a $\pi$-pulse (${\omega }_p$) probes the $0\mathrm{\text{−}}\uparrow$ transition. (b) Dressed-states picture. The basis states are labeled $|\zeta ,n⟩$, where $\zeta$ is the excitonic state, and $n$ the photon number. The states $\mid \uparrow ,N⟩$, $|2X,N-1⟩$ detuned by $\hslash {\delta }_c$, are coupled by the Rabi energy $\hslash {\Omega }_c$ of the control pulse, forming a pair of dressed states $|\alpha ⟩$, $|\beta ⟩$ with a Rabi splitting $\hslash {\Omega }_R$. The control pulse also couples the $|0,N⟩$ and $\mid \downarrow ,N-1⟩$ bare states far from resonance, resulting in an ac-Stark shift of the $|0,N⟩$ state.

Figure 2

Measurements with temporally overlapped spectrally narrow pulses of identical duration. (a) Grayscale plot of photocurrent versus probe detuning, versus pulse area of control pulse with zero detuning ${\delta }_c=0$. (b) Grayscale plot of photocurrent versus probe detuning, versus detuning of a control of pulse area ${\Theta }_c=5\pi$. Green dashed-dot lines indicate energies of the $0\mathrm{\text{−}}\uparrow$ and $0\mathrm{\text{−}}2X$ transitions. The red-lines are fits to [Eqs. (1, 2)], and blue lines show the fit without ac-Stark shift. (c, d) Numerical simulations of (a),(b) with no fitting parameters. A gray scale offset removes the background signal.

Figure 3

Time-resolved measurements of Autler-Townes splitting. (a)–(c) Gray scale plot of photocurrent versus probe detuning versus time-delay $\tau$ at various detunings of the control pulse. Red lines show the effective Rabi energies of the control pulse in time. (d)–(f) Simulations of (a)–(c).

Figure 4

Beats between dressed states of $\uparrow$ and $2X$, or time-resolved measurements of a exciton-biexciton Rabi oscillation. The change in photocurrent $\Delta \mathrm{PC}(\tau )=\mathrm{PC}(\tau )-\mathrm{PC}(-\infty )$ is measured as a function of the time delay $\tau$, for a slow control and fast probe pulses ($T_c=4\mathrm{ps}$, $T_p=1.072\mathrm{ps}$) for various pulse areas ${\Theta }_c$ of the control pulse. Lines show fits to data. Dashed line traces envelope of control pulse.