Coherent and phase-sensitive phenomena of ultrashort laser pulses propagating in three-level Λ -type systems studied with the finite-difference time-domain method

Propagation of single- and two-color hyperbolic secant femtosecond laser pulses in a three-level Λ-type quantum system is investigated by solving the Maxwell and density matrix equations with the finite-difference time-domain and Runge-Kutta methods. As a first study of our modeling, we simulate pulse self-induced transparency (SIT) in two-level systems and see how this phenomenon can be controlled by manipulating the initial relative phase between the SIT pulse and a second control pulse, provided the ratio between both pulse frequencies obeys the relation ω₁∕ω₂=3. We then examine frequency down-conversion processes that are observed with single- and two-color pulses the envelope area of which is equal to or a multiple of 2π, for pulse frequencies close to resonance with the transitions of a three-level Λ medium. Also, phase-sensitive phenomena are discussed in the case of two-color ω-3ω pulses propagating resonantly in the three-level system. In particular, possibilities for such coherent control are found for frequency down-conversion processes when the ratio of the frequencies of optical transitions is ω₁₃∕ω₁₂=3. The conditions for quantum control of four-wave mixing processes are also examined when the pulse frequencies of two-color ω-3ω pulses are far from any resonance of the three-level system. We demonstrate the possibility to cancel the phase sensitivity of the four-wave coupling in a Λ-type system by competition effects between optical transitions.