Harvesting, Coupling, and Control of Single-Exciton Coherences in Photonic Waveguide Antennas

We perform coherent nonlinear spectroscopy of individual excitons strongly confined in single InAs quantum dots (QDs). The retrieval of their intrinsically weak four-wave mixing (FWM) response is enabled by a one-dimensional dielectric waveguide antenna. Compared to a similar QD embedded in bulk media, the FWM detection sensitivity is enhanced by up to 4 orders of magnitude, over a broad operation bandwidth. Three-beam FWM is employed to investigate coherence and population dynamics within individual QD transitions. We retrieve their homogenous dephasing in a presence of low-frequency spectral wandering. Two-dimensional FWM reveals off-resonant Förster coupling between a pair of distinct QDs embedded in the antenna. We also detect a higher order QD nonlinearity (six-wave mixing) and use it to coherently control the FWM transient. Waveguide antennas enable us to conceive multicolor coherent manipulation schemes of individual emitters.

Figure 1

Nanowire antenna for enhancing the four-wave mixing (FWM) response of excitonic transitions strongly confined in InAs QDs. (a) SEM image of a suspended photonic trumpet, which is made of GaAs and embeds a few self-assembled InAs QDs close to its base (inset). This photonic structure simultaneously improves the incoupling of the resonant driving pulses to the QDs and the outcoupling of the nonlinear signal to the collection optics. Also see Sec. A in the Supplemental Material [19]. (b) Spectrally resolved FWM amplitude (violet) and phase (orange). The pulse sequence of Fig. 2 is employed, with ${\tau }_{12}=10\mathrm{ps}$, $({\theta }_1,{\theta }_2)=(\pi /5,2\pi /5)$. The excitation spectrum is given with a gray line. (c) FWM amplitude as a function of ${\mathcal{E}}_1$ pulse area ${\theta }_1\propto \sqrt{P_1}$, showing Rabi oscillation at $GX$ (green circles) and $XB$ (blue squares) transitions. The open symbols give the noise floor. The theoretical predictions appear as solid lines. Measurement parameters: ${\theta }_2=0.82\pi$, ${\tau }_{12}=5\mathrm{ps}$.

Figure 2

Coherence and population dynamics in the exciton-biexciton system of QD1. (a) Coherence dynamics is investigated via degenerate FWM. The top panel indicates the pulse sequence and the related observable. The dependence of the FWM signal on ${\tau }_{12}$ yields $T_2$ and $\sigma$, for both $GX$ and $XB$ transitions. Applied pulse areas: $({\theta }_1,{\theta }_2)=(\pi /5,2\pi /5)$. (b) Population dynamics is investigated via nondegenerate FWM (top panel). The dependence of the FWM signal on ${\tau }_{23}$ yields $T_1$ for $X$ and $B$ states. Measurement parameters: ${\tau }_{12}=1\mathrm{ps}$, $({\theta }_1,{\theta }_2,{\theta }_3)=(\pi /2,\pi /2,\pi /2)$. Both graphs feature logarithmic vertical scales.

Figure 3

Coherent, off-resonant coupling between QD1 and QD2. We investigate here degenerate FWM [pulse sequence shown in Fig. 2] with a nonperturbative driving: $({\theta }_1,{\theta }_2)=(\pi /2,\pi )$. (a) Delay dependence of the FWM amplitude for $GX$, $XB$ (QD1), and $ET$ (QD2). (b) Amplitude of the two-dimensional FWM: coherent coupling is evidenced by a pair of off-diagonal peaks, forming square features depicted with the dashed lines. Note the presence of the diagonal peak for $XB$ induced by the nonperturbative driving. Logarithmic scale over 2 orders of magnitude, given by the bar. Top: FWM amplitude and phase of the off-diagonal peaks, labeled $\alpha$ and $\beta$ at $\omega =(1329.8,1336.16)\mathrm{meV}$ and the diagonal $ET$ peak.

Figure 4

Three-pulse coherent control of the exciton-biexciton system in QD1. (a) A sketch of the pulse sequence and their areas employed to drive the SWM and to manipulate the FWM transient via the FWM to SWM conversion scheme. (b) Top: SWM spectrum of $GX$ and $XB$: $({\tau }_{12},{\tau }_{23})=(15,30)\mathrm{ps}$, $({\theta }_1,{\theta }_2,{\theta }_3)=(\pi /2,\pi ,\pi )$. Middle: Coherent control of the $GX$ and $XB$ by FWM to SWM switching: ${\theta }_3=0$ and ${\theta }_3=\pi$ correspond to blue and red spectra, respectively. Bottom: Manipulation of the FWM spectral response of the $GX$ and $XB$: ${\theta }_3=\pi$, ${\tau }_{23}=30\mathrm{ps}$. (c) Conversion of the FWM to SWM observed on the $GX$ in time domain: ${\theta }_3=\pi$, ${\tau }_{23}=30\mathrm{ps}$.