Enhanced frequency conversion of nonadiabatic resonant pulses in coherently preparedΛsystems

Abstract

We show that nonadiabatic, resonant amplitude- and phase-modulated pulses can be frequency converted with greater efficiency than adiabatic resonant pulses in a coherently prepared $\ensuremath{\Lambda}$ system. Indeed, conversion efficiencies close to unity, similar to those achieved using highly detuned pulses, can been obtained by using highly nonadiabatic resonant pulses. Moreover, by solving the Maxwell-Bloch equations using Fourier transforms, we derive analytical expressions for the probe and the generated four-wave mixing (FWM) pulses as a function of time and propagation distance. From these expressions, which are valid for either adiabatic or nonadiabatic pulses, we derive the result that starting from a nonadiabatic probe pulse, an asymptotically matched probe-FWM pulse pair with the same shape as the initial probe pulse is obtained. In addition, we show that, starting with a nonadiabatic matched pulse pair or a pair of matched pulse trains, we obtain propagation of these pulses without either deformation or losses.