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

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.