Abstract
Quantum control of the four-wave mixing produced by two-color $\ensuremath{\omega}\text{\ensuremath{-}}3\ensuremath{\omega}$ femtosecond laser pulses propagating in a two-level system is accomplished by varying the relative phase between the two laser pulses. The phase sensitivity of the spectral $5\ensuremath{\omega}$ anti-Stokes component is cancelled when the ac Stark shift produced by the $\ensuremath{\omega}$ and $3\ensuremath{\omega}$ pulses is compensated. We apply perturbation theory and provide simple analytical formulas for the phase-sensitivity cancellation in the $5\ensuremath{\omega}$ anti-Stokes component. We demonstrate that this quantum interference effect is robust against chirping of the pulses and show that asymmetric chirping results in phase-sensitive shaping of the four-wave mixing spectra.
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