Coherent control in a single semiconductor quantum dot exhibiting excitonic and biexcitonic features

We have developed a simplified theoretical model to analyze the phenomenon of coherent control in a single semiconductor quantum dot excited by a pair of optical pulses. The first pulse populates a biexciton state by two-photon absorption while the second pulse generates population in the exciton state via deexcitation from the biexciton state. We have used density-matrix analysis for a 3-level system to calculate the time dependent biexciton and exciton state populations. The usual 9x9 matrix has been reduced to a 6x6 matrix. The time variation of the population in each state and it's dependence on the pulse delay manifest coherent control. Numerical estimates made for In0.5Ga0.5As/GaAs single quantum dots qualitatively agree with the recent experimental results.