The interaction of strong laser fields with atoms and molecules provides critical opportunities for observing and controlling photoelectron dynamics on ultrafast timescales. The attoclock technique has significantly advanced the study of attosecond-scale electron tunneling dynamics, enabling the effective extraction of tunneling time delay through photoelectron momentum distributions (PMDs) in elliptically polarized laser fields. Over the past decade, studies on attoclock have gradually expanded from the infrared to the ultraviolet (UV) regime, and an above-threshold ionization (ATI) order-dependent photoelectron angular shift in UV attoclock measurements has been observed. However, the physical mechanisms behind this phenomenon remain unclear, including whether ATI order-dependent angular deflections correlate with tunneling time delays and whether changes in electron energy affect the extraction of tunneling time. Using the time-dependent Schr?dinger equation (TDSE), nonadiabatic model, and model potential (MP) theory, we investigated the PMDs of argon atoms in 400 nm elliptically polarized laser fields. From these results, we extracted the ATI order-dependent photoelectron angular distributions (PADs) and further obtained the tunneling time delay of argon atoms.

To simulate the photoelectron momentum distributions of argon ionized by an elliptically polarized (EP) laser field with ultraviolet laser wavelength of 400 nm, we numerically solved the three-dimensional TDSE in length gauge, as well as two other theoretical methods, i.e., nonadiabatic model and MP theory. For the time evolution of the electrons after the laser ends, we used Kepler’s laws to get the asymptotic momenta.

Fig. 1 provides the PMDs calculated using the three theoretical methods under different laser intensities. The simulations are performed with a laser wavelength of 400 nm, intensities of 1.5×1014 W/cm2, 2.5×1014 W/cm2, and 3.0×1014 W/cm2, and an ellipticity of 0.71. All PMDs demonstrate that both the nonadiabatic model and MP theory can qualitatively reproduce the TDSE simulation outcomes, revealing the crucial role of nonadiabatic effects in electron dynamics. Fig. 2 displays the photoelectron energy spectra (PES) at each intensity. Fig. 3 presents the PADs of different-order ATI rings at 2.5×1014 W/cm2. As the ATI order increases, the angular distributions shift towards larger angles. The three theoretical models all qualitatively reproduce this ATI order-dependent angular shift phenomenon. Compared with the nonadiabatic model, the MP theory exhibits a modulation effect on the electron angular distribution, causing the final-state angular distribution to shift towards smaller angles. Fig. 4 shows the dependence of the peak angles of different ATI rings on photoelectron energy for two intensities (2.5×1014 W/cm2 and 3.0×1014 W/cm2). Fig. 4(a) reveals that the angular peak positions of ATI rings increase with higher ATI orders, while the peak angles decrease for the same ATI order when laser intensity increases. By comparing angular deviations between the nonadiabatic model, MP theory, and TDSE results, we can extract the tunneling time delay of photoelectrons for different ATI rings. Fig. 4(b) shows that the nonadiabatic theory produces predominantly negative angular deviations from TDSE results, leading to a negative tunneling time delay. In contrast, the MP theory yields positive angular deviations, giving a positive tunneling time delay with an upper limit of 15 as. Fig. 5 demonstrates that initial parallel and transverse momentum distributions are strongly dependent on ATI orders. With increasing ATI order, the peak of parallel momentum shifts towards negative values while the peak of transverse momentum moves positively. Concurrently, the tunneling exit moves closer to the nucleus at higher ATI orders. Fig. 6 reveals that electrons with tunneling exits closer to the nucleus experience larger deflection angles, while those exits farther from the nucleus show smaller deflections. Further analysis indicates that the atomic model potential slightly modulates the final-state polarization angles by influencing electron trajectories in the laser field.

We systematically investigate the ATI order-dependent PADs and tunneling time delay in UV attoclock experiments by TDSE, nonadiabatic model, and MP theory. Theoretical calculations generated PMDs of Ar atoms in 400 nm elliptically polarized laser fields, from which we extract the ATI order-dependent PADs. By comparing the results obtained from solving the TDSE and the other two models, we extract an upper limit of tunneling delay for Ar atoms in 400 nm elliptically polarized laser fields at the peak intensity studied, which is 15 as. We find that the tunneling time delay does not vary with increasing ATI orders at higher laser intensities, whereas it decreases with increasing ATI orders at lower laser intensities. The analysis reveals that the tunneling exits and initial momentum distributions induced by MP and nonadiabatic effects jointly influence the final-state PADs in attoclock measurements, thereby affecting the extraction of tunneling time delay.