Two-Photon Coherent Control of a Single Quantum Dot

We report on two-photon coherent control of the biexciton state in single Stranski-Krastanov CdSe quantum dots. Clear interference patterns are observed at twice the optical frequency. The decay of the interference contrast is nonexponential and caused by a dynamical inhomogeneous broadening of the energy levels due to long-term fluctuations in the dot environment.

Figure 1

(a) Scheme of optical transitions and their polarization in a QD with in-plane anisotropy. The exciton ground state $|X⟩$ is split by electron-hole exchange in the substates $|X{⟩}_x$ and $|X{⟩}_y$. (b) Optical layout of the stabilized Michelson interferometer allowing us to adjust the delay between two pulses on two time scales $t_F$ and $t_C$.

Figure 2

Laser and PL spectra from a 100 nm mesa under pulsed excitation recorded in different polarization configurations, ($e_{\mathrm{exc}}$,$e_{\det }$) denote polarization of excitation and detection, respectively. Directions $x$ and $y$ are along [110] and $[1\overline{1}0]$. The excitation energy is 2.437 eV. Inset: Integral PL yield of exciton and biexciton recombination versus excitation power. The solid curve is a fit with $I\propto 1-e^{-A{P}^2}$ ($A=0.013$) accounting for the depletion of $|g⟩$.

Figure 3

Coherent control interferograms for exciton ($X$) and biexciton ($XX$) PL (first and second row) and for line $E$ (last row), for pulses overlapping [column (a)] and separated in time [column (b)]. In column (c) are shown two-dimensional plots in the photon energy–delay time plane extracted from the same spectra as in column (b).

Figure 4

Contrast $c$ as a function of the pulse delay $t_C$, (a) biexciton emission of QD#1 (same as in Figs. 2, 3) and (c) biexciton emission of QD#2 as well as for line $E$ of QD#3. The contrast of the laser is shown with open symbols. The corresponding PL lines $X$ and $XX$ of QD#1 (b) and QD#2 (d) are measured with a resolution of $35\mu \mathrm{eV}$. The solid curve in panel (a) is the numerically calculated Fourier transform of the exciton band in (b) taken in (${\pi }_x,{\pi }_x$) polarization. For QD#2 Gaussian fits of the contrast [solid curve in (c)] and the spectral line shape of $X$ [dotted line in (d)] give FWHM of 12 ps and $8\ln (2)\hslash {\Gamma }_X^{-1}=16\mathrm{ps}$, respectively. The upper line in (c) is an exponential fit for $E$.