Carrier-envelope phase dependent photoelectron energy spectra in low intensity regime

We study the carrier-envelope phase (CEP) dependent photoelectron energy spectra from above-threshold ionization by numerically solving the time-dependent Schrödinger equation of hydrogen atom in a few-cycle laser field at intensities in the range of (2-10) × 10¹³ W/cm². Depending on the electron energy and the laser intensity, the yield of the photoelectron reveals clear oscillations with respect to the CEP. At high laser intensities (larger than ~3 × 10¹³ W/cm²), the yield of the high-energy photoelectrons (larger than 2U_p, with U_p being the ponderomotive potential) shows two kinds of oscillations with the CEP for different electron energies. There is a clear phase jump for those two kinds of oscillations. In contrast, at low laser intensities (smaller than ~3 × 10¹³ W/cm²), the phase of the oscillation for the high-energy photoelectron yield with the CEP is nearly independent on the electron energy, which will reduce the sensitivity of the retrieval of single-shot CEP using the method reported by T. Wittmann et al. [Nat. Phys. 5, 357 (2009)] at low laser intensities. We further show that the low-energy photoelectrons display distinct CEP-dependent intercycle interference fringes, providing an alternative approach to retrieve the CEP with high sensitivity in a few-cycle laser field with low intensity.