Coherent nonlinear interference effect for devices of long-term memory with femtosecond pulses

Computer simulation of the response (polarization) of three-level systems (for example, of quantum dots) with the common upper level (the Λ-scheme) was carried out for devices of long-term memory with femtosecond driving and signal pulses. For producing an efficient response, the pulse area should be on the order of π. Under the action of the first driving pulse on the 1–2 transition and the simultaneous action of the probe pulse on the 3–2 transition, a long-lived polarization with the lifetime dependent on the lifetimes of the lower (1 and 3) levels appears owing to the nonlinear interference effect. Under the action of the second driving pulse, a signal pulse appears on the 3–2 transition, whose amplitude is proportional to the amplitude of the input probe pulse and exponentially decreases with the delay time between the first and the second driving pulses. The set of equations for the density matrix was solved numerically in the semiclassical approximation and in the rotating wave approximation. The temporal evolution of the nondiagonal matrix elements reflects the temporal evolution of the nonlinear polarization. The polarization spectrum is found by the Fourier transform of the time dependence of the nondiagonal elements. The polarization spectrum (the power spectrum) possesses an interference structure with a fringe period governed by the delay time between the first and the second driving pulses. The inverse Fourier transform reconstructs the temporal shape of the pulses.