Theory of time-resolved Raman scattering and fluorescence emission from semiconductor quantum dots

We present a microscopic description of time-resolved Raman scattering and fluorescence emission of a coupled phonon-quantum dot system. Using density matrix formalism and higher-order Born approximation, the optical emission and scattering spectra of an InGaAs/GaAs-quantum dot are calculated for stationary and pulsed optical excitation. By means of their characteristic decay times, contributions such as Rayleigh, Raman, and fluorescence can be distinguished.

Figure 1

(Color online) Measurement setup.

Figure 2

(Color online) Operator scheme: straight arrows correspond to photon operators ($c_{\mathbf{k}}^{†}$: emission of a photon), where the length of the straight arrows stands for the energy of the emitted photon. The expectation values correspond to the probability of the processes, depicted by the straight arrows on the right in each subfigure. Curved arrows stand for phonons $b_{\mathbf{q}}/b_{\mathbf{q}}^{†}$. Within a phonon-assisted process, the energy of the emitted photon can be redshifted ($b^{†}$: phonon-emission) or blueshifted ($b$: phonon absorption) with respect to the unperturbed process.

Figure 3

Photon flux as calculated with Eq. (5) for excitation with a stationary laser pulse at $T=77\text{K}$.

Figure 4

(Color online) Time-resolved emission spectrum of an InGaAs/GaAs-QD after excitation with a coherent Gaussian pulse with 2 ps temporal width. The spectrum is plotted between 0 and 20 ps at a temperature of 77 K and time resolution of $\Delta t=400\text{fs}$. The main fluorescence peak at the band gap energy is set to 0 meV.

Figure 5

(Color online) Time evolution of the fluorescence (solid line), Stokes-phonon replica (dotted line), Rayleigh (dashed line), and Raman (dotted-dashed line) scattering contributions under excitation with a laser pulse (FWHM of 2 ps). For comparison, Rayleigh and fluorescence as well as the phonon-assisted processes are normed to one height, respectively.

Figure 6

(Color online) Time evolution of the conduction-band density (solid line) and the square of the microscopic polarization (dashed line).