Raman coherence beats from the entangled state involving polarized excitons in single quantum dots

The optically induced and detected entangled state involving an exciton Zeeman doublet with entanglement entropy as high as $\sim 0.7$ was created using picosecond lasers in single $\mathrm{GaAs}$ quantum dots. The temporal evolution of the nonradiative Raman coherence between two exciton states was directly resolved in quantum beats measured in the homodyne detected differential transmission experiment. The Raman coherence time, $66\pm 15\mathrm{ps}$, was determined from the decay of the envelope of the quantum beats, and was found to be limited by the lifetimes of the exciton transitions, $50\pm 3\mathrm{ps}$.

Figure 1

In the presence of a modest magnetic field applied along the growth direction, two excitons with orthogonal polarizations can be excited within a single dot. In the excitation picture, $G$, $X$, $BX$, and $TX$ represent the crystal ground state, the exciton, the biexciton and the virtual two-exciton state, respectively. The biexciton binding energy, $\Delta$, is much larger than the laser bandwidth. Therefore, the problem is reduced to a V system enclosed in the box.

Figure 2

(b) Sum and (c) difference of the ${\mathrm{DT}}_{\mathrm{CLP}}$ and ${\mathrm{DT}}_{\mathrm{OLP}}$ with the original data shown in (a). Solid lines are theoretical fits to the data with an exponential function in (b) and a decaying cosine function in (c). The data shown in (d) is obtained in similar experiments with a higher pump power. The Raman coherence time is reduced at higher excitation power most likely due to the increased scattering of the resonantly excited exciton from nearly degenerate delocalized states (Ref. 16).