Resolving strong-field tunneling ionization with a temporal double-slit interferometer

Laser-induced tunneling ionization is one of the most fundamental and ubiquitous quantum processes and it initiates various ultrafast phenomena in intense laser-atom and laser-molecule interactions. Accurately resolving tunneling ionization is essential for understanding these phenomena. Based on the advanced attosecond technologies, such as high-order harmonic spectroscopy and strong-field photoelectron holography, previous studies have resolved the temporal properties of the tunneling process for rescattering electron. Here, as a complement, we theoretically demonstrate the retrieval of the time information of the tunneling process for the direct electron with the temporal double-slit interferometer. In this scheme, a weak second harmonic parallel to the fundamental field is added. By solving the time-dependent Schr\"odinger equation, the photoelectron momentum distribution (PEMD) from strong-field tunneling ionization is obtained. Varying the relative phase of the parallel two-color field, the path of the ionized electrons periodically changes, leading to a shift of the time double-slit interference fringes in PEMDs. By analyzing the response of the interference fringes to the perturbation, the time information of direct electron in strong-field tunneling ionization is reconstructed. Interestingly, our results present excellent agreement with the complex time obtained from the quantum-orbit model.