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We investigate numerically with Hylleraas coordinates the frequencydependence of the carrier-envelope phase (CEP) effect on bound-boundtransitions of helium induced by an ultrashort laser pulse of few cycles. Wefind that the CEP effect is very sensitive to the carrier frequency of thelaser pulse, occurring regularly even at far-off resonance frequencies. Byanalyzing a two-level model, we find that the CEP effect can be attributed tothe 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 ofthe CEP effect to laser's carrier frequency. Multi-level influence on the CEPeffect is also discussed.

Sensitive frequency-dependence of the carrier-envelope phase effect on bound-bound transition: an interference perspective