Polarization-Dependent Interference of Coherent Scattering from Orthogonal Dipole Moments of a Resonantly Excited Quantum Dot

Resonant photoluminescence excitation (RPLE) spectra of a neutral InGaAs quantum dot show unconventional line shapes that depend on the detection polarization. We characterize this phenomenon by performing polarization-dependent RPLE measurements and simulating the measured spectra with a three-level quantum model. The spectra are explained by interference between fields coherently scattered from the two fine structure split exciton states, and the measurements enable extraction of the steady-state coherence between the two exciton states.

Figure 1

(a) Quantum dot energy diagram. The population spontaneous decay rate is determined to be ${\mathrm{\Gamma }}_{\mathrm{sp}}/2\pi =(279.2\pm 0.9)\mathrm{MHz}$ by time-resolved fluorescence measurements (see Supplemental Material [24]), and the fine structure splitting is ${\mathrm{\Delta }}_{\mathrm{FSS}}/2\pi =(2.869\pm 0.001)\mathrm{GHz}$. (b) Polarization and electric dipole moment orientations. The lower-energy ${\mathit{d}}_1$ and higher-energy ${\mathit{d}}_2$ dipole moments are shown, as is the polarization of the excitation field ${\mathit{E}}_0$. The shape of the QD is shown schematically with its asymmetry exaggerated.

Figure 2

Example RPLE spectra recorded with ${\mathrm{\Omega }}_R=3.57{\mathrm{\Gamma }}_{\mathrm{sp}}$ and detection polarization chosen to be (a) $X$ (blue points), (b) $Y$ (orange points), or (c) to eliminate either the low-energy or high-energy peak. The black solid lines in (a) and (b) are fittings following Eqs. (1) and (2). The green (solid) and red (dashed) lines underneath the spectra are the calculated portions of coherent and incoherent scattering, respectively. The two yellow curves in (c) are the fittings obtained by using the calculated exciton populations ${\rho }_{11}^{\infty }$ and ${\rho }_{22}^{\infty }$ from the three-level model. (d) The coherence $\mathrm{Re}[{\rho }_{12}^{\infty }]$ extracted from the curves in (a) and (b); the colors indicate the polarization whence the coherence was extracted. The black solid curve in (d) is not a fit but the calculation of $\mathrm{Re}[{\rho }_{12}^{\infty }]$ using the same parameters found in the previous fittings in (a) and (b).

Figure 3

$\mathrm{Re}[{\rho }_{12}^{\infty }]$ extracted at different excitation powers. The curves are vertically offset for clarity. The color scheme used in each pair is the same as Fig. 2; i.e., orange is extracted from the $Y$-polarized RPLE and blue from the $X$-polarized RPLE. The black solid curves are the calculation of $\mathrm{Re}[{\rho }_{12}^{\infty }]$ at different Rabi frequencies ${\mathrm{\Omega }}_R$ determined by fittings to the raw RPLE data similar to Figs. 2 and 2. The other model parameters are the same throughout all the calculations. Inset: Rabi frequency ${\mathrm{\Omega }}_R$ versus the square root of the excitation power. The red straight line is a linear fit with a slope of $(0.806\pm 0.011){\mathrm{\Gamma }}_{\mathrm{sp}}/\sqrt{\mu W}$.

Figure 4

(a) The evolution of the high-energy state’s intrinsic resonance frequency ${\omega }_2/2\pi$ (blue open circles) and the evolution of the peak positions of the excited population ${\rho }_{22}^{\infty }$ obtained by either a Lorentzian fitting (blue dots) or the $V$-system simulation (blue line). (b) The evolution of the low-energy state’s intrinsic resonance frequency ${\omega }_1/2\pi$ (red open circles) and the evolution of the peak positions of the excited population ${\rho }_{11}^{\infty }$ obtained by either a Lorentzian fitting (red dots) or the $V$-system simulation (red line).