Nonequilibrium dynamics in an optical transition from a neutral quantum dot to a correlated many-body state

We investigate the effect of many-body interactions on the optical absorption spectrum of a charge-tunable quantum dot coupled to a degenerate electron gas. A constructive Fano interference between an indirect path, associated with an intradot exciton generation followed by tunneling, and a direct path, associated with the ionization of a valence-band quantum dot electron, ensures the visibility of the ensuing Fermi-edge singularity despite weak absorption strength. We find good agreement between experiment and renormalization group theory, but only when we generalize the Anderson impurity model to include a static hole and a dynamic dot-electron scattering potential. The latter highlights the fact that an optically active dot acts as a tunable quantum impurity, enabling the investigation of a new dynamic regime of Fermi-edge physics.

Figure 1

(a) Differential transmission measurements of the $X^0$ and the $X^{-}$ (inset) QD charging states, after subtracting the dc Stark shift (Ref. 27). $\Delta E=E-E_0$ incorporates the peak absorption energy $E_0=1.3913$ eV at $V_g=0.52$ V. (b) High-resolution laser absorption scans (color scale) at selected gate voltages. Solid lines show fits of the calculated lowest-energy peak position, $\Delta E_{\mathrm{peak}}$, either without the scattering potential ($H_{\text{S}}^a=0$, solid gray), or including it ($H_{\text{S}}^a\ne 0$, solid black). Dashed lines show the ground state energy difference, $\hslash {\omega }_{\mathrm{th}}$, between the initial and final states of the absorption process, calculated for $H_{\text{S}}^a=0$ (dashed gray) or $H_{\text{S}}^a\ne 0$ (dashed black). The difference $\Delta E_{\mathrm{peak}}-\hslash {\omega }_{\mathrm{th}}$ is on the order of the dark-bright splitting ${\Delta }_E$ in the plateau center. (c) Comparison of the measured (dots) and calculated (curve) maximum absorption amplitudes (the latter scaled vertically by an overall fixed oscillator strength), shown as a function of gate voltage. (d)–(i) Measured absorption line shapes of the transition from a neutral exciton to a correlated many-body state (normalized by the experimental peak height $A_{\max }$) at gate voltages indicated by corresponding color-coded arrows in (b). The green curves display calculated results, scaled vertically and shifted horizontally to minimize the ${\chi }^2$ value of each fit (Ref. 27). The absorption components of the direct (red dashed), indirect (blue dotted), and interference (orange dash-dotted) terms are exemplarily depicted in (i). Since the tail of the $X^0$ state spectrally overlaps with the $X^{+}$ state, we can excite the latter, which shows up as a dip in the absorption line shapes for red detunings. (j) Schematic of the renormalized transition energies of the bright ${\varepsilon }_F-{\Delta }_{\mathrm{b}}$ and dark ${\varepsilon }_F-{\Delta }_{\mathrm{b}}-{\Delta }_E$ electron levels with respect to the Fermi energy ${\varepsilon }_{\mathrm{F}}$ directly after the single-photon absorption event. ${\Delta }_{\mathrm{b}}$ indicates the energy difference between the Fermi energy and the bright state, corresponding to the line shape shown in (d) (top), in (f) (middle), and in (i) (bottom).

Figure 2

Scheme of the quantum impurity system consisting of a single QD and a nearby FR. (a) Initial quantum state where the QD with energy ${\varepsilon }_0$ above the Fermi energy ${\varepsilon }_{\text{F}}$ is empty and the FR is unperturbed. The absorption of a single photon leads either (b) to a bound exciton on the QD or (c) to an indirect exciton. (d) The final state as $t\to \infty$ involves many-body correlations (red) between the FR and the QD. The black dashed and dotted lines depict the scattering potential between QD and FR, or the intradot Coulomb attraction, respectively.

Figure 3

Comparison of the experimental absorption line shape at $V_g=0.482$ V with theory assuming different scattering scenarios. For the scales, the same conventions were used as for Figs. 1d, 1e, 1f, 1g, 1h, 1i. The red dashed line shows the best fit for the EAM model ($H_{\text{S}}^a=0$). Neglecting the electron-electron repulsion ($H_{\text{S}}^a\ne 0$ with $G_{\text{ee}}=0$) the best fit yields the blue dotted curve, while the mean-field approach ($H_{\langle S\rangle }^a$) is shown by the orange dash-dotted curve. The green solid line depicts a dynamic scattering potential.