Jia Tan^{1、†}, Shengliang Xu^{1}, Xu Han^{1}, Yueming Zhou^{1、*}, Min Li^{1}, Wei Cao^{1}, Qingbin Zhang^{1、*}, and Peixiang Lu^{1、2、*}

Author Affiliations
^{1}Huazhong University of Science and Technology, School of Physics and Wuhan National Laboratory for Optoelectronics, Wuhan, China^{2}Wuhan Institute of Technology, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan, Chinashow less

Abstract

Tunneling ionization of atoms and molecules induced by intense laser pulses contains the contributions of numerous quantum orbits. Identifying the contributions of these orbits is crucial for exploring the application of tunneling and for understanding various tunneling-triggered strong-field phenomena. We perform a combined experimental and theoretical study to identify the relative contributions of the quantum orbits corresponding to the electrons tunneling ionized during the adjacent rising and falling quarter cycles of the electric field of the laser pulse. In our scheme, a perturbative second-harmonic field is added to the fundamental driving field. By analyzing the relative phase dependence of the signal in the photoelectron momentum distribution, the relative contributions of these two orbits are unambiguously determined. Our results show that their relative contributions sensitively depend on the longitudinal momentum and modulate with the transverse momentum of the photoelectron, which is attributed to the interference of the electron wave packets of the long orbit. The relative contributions of these orbits resolved here are important for the application of strong-field tunneling ionization as a photoelectron spectroscopy for attosecond time-resolved measurements.$$\mathrm{ND}(\mathbf{p};\phi )=\frac{Y(\mathbf{p};\phi )-{Y}_{\mathrm{avg}}(\mathbf{p})}{Y(\mathbf{p};\phi )+{Y}_{\mathrm{avg}}(\mathbf{p})},$$ | (1) |

$$\mathrm{ND}(\mathbf{p};\phi )=P(\mathbf{p})\text{\hspace{0.17em}}\mathrm{cos}[\phi -{\phi}_{m}(\mathbf{p})],$$ | (2) |

$$\mathrm{ND}(\mathbf{p};\phi )=\alpha \text{\hspace{0.17em}}\mathrm{cos}[\phi -{\phi}_{m}^{\mathrm{L}}(\mathbf{p})]+\beta \text{\hspace{0.17em}}\mathrm{cos}[\phi -{\phi}_{m}^{\mathrm{S}}(\mathbf{p})],$$ | (3) |