Effect of the Stark shift on the low-energy interference structure in strong-field ionization

An improved quantum trajectory Monte Carlo method including the Stark shift of the initial state, Coulomb potential, and multielectron polarization-induced dipole potential is adopted to revisit the origin of the low-energy interference structure in the photoelectron momentum distribution of the xenon atom subjected to an intense laser field, and resolve the different contributions of these three effects. We found that the Stark shift plays an essential role on the low-energy interference structure, which moves the ringlike constructive interference structure to the lower momentum region. The formation of the low-energy interference structure is a result of the combined effects of Stark shift, laser, and Coulomb fields, while the multielectron polarization mainly enhance the probability of the low energy photoelectron spectrum. Our finding provides insight into the electron dynamics of atoms and molecules when driven by the intense laser fields.

Figure 1

Simulated two-dimensional (2D) photoelectron momentum spectra of a Xe atom ionized by a laser pulse with a duration of $n=8$ cycles, at a wavelength of 800 nm. (a) and (d) $I=1.05\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ corresponding to the Keldysh parameter $\gamma =0.9829$, (b) and (e) $I=1.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, $\gamma =0.8223$, and (c) and (f) $I=2.0\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, $\gamma =0.712$. The left column [(a)–(c)]: QTMC calculations considering only the Coulomb potential. The right column [(d)–(f)]: IQTMC calculations considering the Coulomb potential, Stark shift, and MEPIDP.

Figure 2

LEIS ($P_r\in [0,0.27]$ a.u.) in the photoelectron momentum spectra. (a) and (b) TDSE simulations with model potential (a) and Coulomb potential (b), respectively. (c) Results of the IQTMC calculations (d)–(h) semiclassical simulations with (d) SAF simulation; (e) only laser field and Stark shift are included; (f) only laser field and Coulomb potential are included; (g) with inclusion of laser field, Coulomb potential, and MEPIDP; and (h) with inclusion of laser field, Coulomb potential, and Stark shift. The color scales have been normalized for comparison. The laser parameters are the same as those in Figs. 1 and 1.

Figure 3

(a) Subcycle time windows in which photoelectrons contributing to the momentum distributions ($P_x\ge 0$ a.u.) of the low-energy part. (b) and (c) The half-plane momentum spectrum with (b) and without (c) Stark shift. ($P_x\ge 0$ a.u.) (d) and (e) Final phase distributions of the electron trajectories emitted from different time windows denoted by the same color in (a). (f) and (g) The phase calculated by the integral terms, i.e., the second term in Eqs. (11) and (14), respectively. (h) and (i) Initial phase related to ionization potential, i.e., the first term in Eqs. (11) and (14), respectively. (j) Energy spectrum of photoelectron with (red solid line) and without (blue dotted line) considering the Stark shift.

Figure 4

(a) and (b) The momentum distributions ($P_x\ge 0$ a.u.) with (a) and without (b) considering the MEPIDP. (c) The initial ionization phase analysis of electron contributing to the final momentum indicated by a black rectangle in (a) and (b).