Temperature dependency of resonance fluorescence from InAs/GaAs quantum dots: Dephasing mechanisms

We report a study on temperature-dependent resonant fluorescence from InAs/GaAs quantum dots. We combined spectral and temporal measurements in order to identify sources of dephasing. In the spectral domain, we observed temperature-dependent broadening of the zero-phonon line as $0.3\mu \mathrm{eV}/\mathrm{K}$, and a temperature-dependent phonon broadband. Time-resolved autocorrelation measurements revealed temperature-dependent spin pumping times between $T_{1,s}=6$ ns (4 K) and $0.5$ ns (15 K). These results are compared against theoretical modeling with a master equation for a four-level system coupled to phonon and spin baths. We explained the results by phonon-mediated hole-spin scattering between two excited states, with the piezophonons as a dominant mechanism.

Figure 1

In (a) and (c), high-resolution FPI spectra of ZPL at $T=4$ K for two excitation powers below and above saturation $\mathrm{\Omega }=0.6{\mathrm{\Omega }}_S$ and $\mathrm{\Omega }=4{\mathrm{\Omega }}_S$, respectively. Data are plotted together with independent Lorentzian fits to inelastic (red curve) and total (blue curve) intensity. In (b) and (d), the same as (a) and (c) but at $T=15$ K. (d) Inset: Saturation curves at $T=4$ and 15 K, together with fits (solid lines). In (e), $\kappa$ of inelastic peak for $0.6{\mathrm{\Omega }}_S$ (black squares) as a function of temperature, together with fits to the data (red curve). (e) Inset: Rabi frequency $\left({\mathrm{\Omega }}_R\right)$ at $T=4$ and 15 K as a function of temperature with linear fits. In (f), elastic to total ratio for $T=4$, 10, and 15 K as extracted from FP data, together with fits; for more discussion, see text.

Figure 2

Spectrometer data for $T=4$ (black squares), 10 (red squares), and 15 K (green squares), are plotted together with corresponding fits (solid lines of the same color) at $\mathrm{\Omega }\propto {\mathrm{\Omega }}_S$. The fitting parameters are $(a_h,a_e)=(1.9,2.1)$ nm, $T_1=0.6$ ns, and ${\mathrm{\Gamma }}^{*}=0.3$ $\mu \mathrm{eV}/\mathrm{K}$. In the inset, the extracted phonon density of states $J\left(\omega \right)$ used for the fits in the main figure. In the right inset, a comparison between $I\left(\omega \right)$ for different electron and hole localization lengths, $(a_h,a_e)=(2,3)$ nm (green line) and $(a_h,a_e)=(1.5,4.5)$ nm (black line), revealing a double Gaussian distribution; see text for discussion.

Figure 3

High-resolution FPI spectra of the zero-phonon line (black squares) normalized to the maximum intensity of the central inelastic peak for two powers $\mathrm{\Omega }=0.6{\mathrm{\Omega }}_S$ (upper row) and $\mathrm{\Omega }=2{\mathrm{\Omega }}_S$ (lower row) at $T=4$ and 15 K. Fits to data using four-level ME Eq. (A1) with (red line) and without (dashed blue line) pure dephasing. Fit parameters for (a) and (b) are listed in Table 1, and for (c) and (d) the same except $T_{1,s}=1/(7\pm 1)$ (4 K) and $T_{1,s}=1/(0.5\pm 0.1)$ (15 K). In the inset, $g^2\left(t\right)$ data (black squares) with fits using the four-level ME with the same set of parameters. Time-dependent fits are convoluted with a detector response function.

Figure 4

Comparison between experimental, $T_{s,h}$, and theoretical, $T_{\text{piezo},T}$, phonon-mediated spin relaxation times for a hole. $T_{\text{piezo},T}$ are calculated after Eq. (1) and plotted as a blue solid line. Errors on $T_{\text{piezo},T}$ are plotted as dashed blue lines. Compare text for more details.

Figure 5

Four-level system coupled to the phonon bath. We use the following notation in the text: $|\uparrow \rangle =|1\rangle ,|\downarrow \rangle =|2\rangle ,|\uparrow \downarrow ,\Downarrow \rangle =|3\rangle ,|\uparrow \downarrow ,\Uparrow \rangle =|4\rangle ,{\mathrm{\Omega }}_R=\mathrm{\Omega }$. Color coding reflects the transition energies: red for low-energy transitions and blue for high-energy transitions.

Figure 6

Simulations illustrating the interplay between different parameters in the model. In the first column, $T_{s,h}=T_{s,e}=4$ ns, in the second column ${\mathrm{\Gamma }}^{*}=1.2\mu \text{eV}$; for details compare text.

Figure 7

Low-power $g^2\left(t\right)$ with fits.

Figure 8

Comparison between pure dephasing and charge noise effects on Mollow triplet spectra for different laser detunings. Top left: No pure dephasing but with charge noise. Top right: Pure dephasing but no charge noise. For charge noise, we used a Gaussian distribution with $\sigma =0.7\mu \text{eV},T_1=0.6$ ns $\text{El}/\text{Tot}$ ratios extracted from data in Sec. 4a. Bottom: Effect of charge noise and pure dephasing on $\text{El}/\text{Tot}$; simulations are plotted against data.