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Phase dependence of electron localization in HeH$^{2+}$ dissociation with an intense few-cycle laser pulse

The electron localization in the dissociation of the asymmetric charged molecular ion HeH$^{2+}$ exposed to an intense few-cycle laser pulse is studied by solving numerically the 3D time-dependent Schrödinger equation. By varying the carrier-envelope phase (CEP) and the intensity of the pulse, the upward shift of the localization probability and the suppression of the dissociation channel He$^{2+}$+H are observed . Our analysis shows that the phenomenon is attributed to the asymmetric structure of the molecule as well as the recollision-assistant field-induced ionization of the electron wave packets localized on H$^+$ in the trailing of the pulse.