Dephasing of InAs quantum dot $p$-shell excitons studied using two-dimensional coherent spectroscopy

The dephasing mechanisms of $p$-shell and $s$-shell excitons in an InAs self-assembled quantum dot ensemble are examined using two-dimensional coherent spectroscopy (2DCS). 2DCS provides a comprehensive picture of how the energy level structure of dots affects the exciton dephasing rates and recombination lifetimes. We find that at low temperatures, dephasing of $s$-shell excitons is lifetime limited, whereas $p$-shell excitons exhibit significant pure dephasing due to scattering between degenerate spin states. At elevated temperatures, quadratic exciton-phonon coupling plays an important role in both $s$-shell and $p$-shell exciton dephasing. We show that multiple $p$-shell states are also responsible for stronger phonon dephasing for these transitions.

Figure 1

(a) Photoluminescence (PL) intensity (blue solid line) from the InAs self-assembled quantum dots, excited with 633-nm CW laser light. A typical excitation laser spectrum used in the 2DCS experiment for $s$-shell excitons is shown as a black line. (b) The illustration for transition in $s$ and $p$ shells. An illustration of the wave functions for electrons and holes is also depicted [40]. (c) Schematic and (d) time-ordering in the 2DCS experiment. Delays between ${\mathrm{A}}^{*}$, B, C, and signal are denoted as $\tau ,T$, and $t$, respectively. (e) Energy structure of exciton-biexciton system and selection rules. (f) Quantum paths for (i)–(iii) colinear (HHHH) and (iv) cross-linear (HVHV) polarization sequence.

Figure 2

Normalized 2D rephasing amplitude spectra for $s$ shell at (a) $T_L$ = 10 and (b) 60 K and for $p$ shell at (c) $T_L$ = 10 and (d) 60 K. The excitation spectrum is depicted by the black solid line in each panel. (e)–(h) Intensity profiles of cross diagonal lines shown as dashed black lines in (a)–(d). Data are shown as red lines and total fits are shown as black lines. Lorentzian fits corresponding to zero-phonon lines, phonon side bands, and biexcitons are shown as blue-, orange-, and green-dashed lines, respectively, in (f) and (h).

Figure 3

Zero-phonon linewidths for (a) $s$-shell and (b) $p$-shell excitons across the inohomogeneous distribution as a function of temperature. Colored regions indicate estimated errors from multiple measurements. Black circles show the center emission energy along inhomogneous distribution at each temperature.

Figure 4

Zero-phonon line weights for $s$ and $p$ shells as a function of temperature.

Figure 5

Rephasing zero-quantum amplitude spectra for (a) $s$ and (b) $p$ shells at $T_L$ = 10 K. [(c) and (d)] Intensity profiles of vertical lines shown as dashed lines in (a) and (b). Red solid lines are data and black dashed lines are Lorentzian fits.

Figure 6

(a) Dephasing and (b) population decay rates for $s$- and $p$-shell excitons as a function of temperature. Pure dephasing rates for (c) $s$- and (d) $p$-shell excitons as a function of temperature. Marks are data and black solid lines are activation fit results. Obtained fitting parameters for $s$- and $p$-shell excitons are shown in (c) and (d), respectively.

Figure 7

Rephasing zero-quantum amplitude spectra for $p$-shell excitons with the polarization sequences of (a) HVHV and (b) $VHVH$. [(c) and (d)] Intensity profiles of vertical lines shown as dashed lines in (a) and (b). Red solid lines are data and black dashed lines are double-Lorentzian fits.