Phonon-induced pure dephasing in exciton-biexciton quantum dot systems driven by ultrafast laser pulse sequences

A semiconductor quantum dot model accounting for single exciton as well as biexciton states coupled to phonons and laser light is investigated in the limit of strong electronic confinement. For an arbitrary sequence of excitations with ultrafast pulses analytical solutions are obtained for all density-matrix elements. The results are nonperturbative with respect to both the carrier-phonon and the carrier-light coupling. Numerical results for a single pulse excitation are presented illustrating spectral features of our solution as well as pulse area and temperature dependences.

Figure 1

Occupations of the ground $\left[C_0\right]$ and the biexciton state $\left[C_B\right]$ as well as the total excitonic occupation $[C_x=C_{+}+C_{-}]$: (a) after ultrafast ${\sigma }^{+}$ excitation with $f_{{\sigma }^{+}}=f$, $f_{{\sigma }^{-}}=0$; (b) after ultrafast excitation with a linearly polarized pulse with $f_{{\sigma }^{+}}=f_{{\sigma }^{-}}=f∕2$, ${\phi }_{{\sigma }^{+}}={\phi }_{{\sigma }^{-}}=\phi$.

Figure 2

Coherent phonon amplitude $A\left(f\right)$ [see Eq. (38)] after excitation with an ultrafast pulse: circularly polarized excitation (solid line); linearly polarized excitation (dashed line); amplitude $\tilde{A}\left(f\right)$ of the optically generated $N^{\mathrm{opt}}$ phonon occupation [see Eq. (42)] after linearly polarized excitation (dash-dotted line); amplitude $A^2\left(f\right)$ of the coherent phonon density $N^{\mathrm{coh}}$ after linearly polarized excitation (dotted line).

Figure 3

Amplitudes of interband coherences ${\tilde{C}}_{0+}$ after circular (dashed) and after linear (solid) excitation; ${\tilde{C}}_{+B}$ after the same linear excitation (dot-dashed).

Figure 4

Background spectra calculated at temperatures $T=\mathrm{1,10,100}\mathrm{K}$ for the ground state to exciton transition $G_{\mathrm{GET}}$, the exciton to biexciton transition $G_{\mathrm{EBT}}$ and the ground state to biexciton transition $G_{\mathrm{GBT}}$. The zero of energy $\hslash \omega =0$ is at the position of the respective ZPLs (vertical lines).