  We investigate numerically with Hylleraas coordinates the frequency
dependence of the carrier-envelope phase (CEP) effect on bound-bound
transitions of helium induced by an ultrashort laser pulse of few cycles. We
find that the CEP effect is very sensitive to the carrier frequency of the
laser pulse, occurring regularly even at far-off resonance frequencies. By
analyzing a two-level model, we find that the CEP effect can be attributed to
the quantum interference between neighboring multi-photon transition pathways,
which is made possible by the broadened spectrum of the ultrashort laser pulse.
A general picture is developed along this line to understand the sensitivity of
the CEP effect to laser's carrier frequency. Multi-level influence on the CEP
effect is also discussed.
