Coherent population control and three-pulse photon echoes: Their dependence on phase of excitation pulse

We discuss analytically here coherent population control and photon echoes of two-level atoms excited by two excitation pulses of different characteristics: (i) the excitation pulses with the same carrier-envelope phases and (ii) the excitation pulses, which are obtained by intensity-modulation of a continuous-wave laser beam and are free from incidental phase- and frequency-modulation. A perturbative calculation, which includes the effect of relaxations during pulse excitations shows that both the coherently controlled population and the echo field show considerably different behaviors depending on the characteristics of the excitation pulses. We also find that the peak position of the echo field can be controlled by adjusting the pulse widths of the excitation pulses.