Absorption of a weak probe in singly charged n-doped quantum dots in the Voigt geometry

We analyze the absorption of a weak probe field in singly charged n-doped quantum dots in the presence of an external magnetic field in the Voigt geometry. The dots are modeled as double lambda systems. A laser field pumps two of the four active transitions while a probe field is applied along the two undriven transitions. It is shown that for both on resonance and out of resonance driving gain (without inversion) is obtained at two sidebands of the dressed QDs. We found that the peak value of gain can be maximized by a proper selection of both the external magnetic field and the Rabi frequency of the pump field for out of resonance driving. We also show that the coherent driving in combination with above-band excitation allows one to turn the absorption peaks into gain (with inversion) in the whole spectral range.