Control of photoelectron interference in asymmetric momentum distributions using two-color laser fields

We theoretically study the control of photoelectron interference of atoms ionized by a two-color laser field with parallel polarizations. Based on both the quantum-trajectory Monte Carlo model and an ab initio simulation with numerically solving the time-dependent Schrödinger equation, we show that the photoelectron angular distributions can be controlled by changing the relative phase of the two frequency components. The high-energy and low-energy photoelectrons show different modulations with respect to the relative phase. Tracing back to the initial coordinates (the ionization time with respect to the laser phase and the initial momentum) of photoelectrons, we have studied the physical origin of the asymmetric structure in photoelectron angular distributions and the dynamics of controlling photoelectron emission using the two-color laser fields. We show that the long tail of the Coulomb potential plays a minor role in the position of the high-energy cutoff in the backward scattering, whereas it is of great importance in the formation of the asymmetric structures of the low-energy photoelectrons.

Figure 1

The typical two-color laser field of Eq. (1) for $\phi =0$. An eight-cycle trapezoidal pulse is used in our calculation with a two-cycle turn on and turn off for 800 nm.

Figure 2

The simulated PADs of H atoms by the QTMC calculations (a) in a linearly polarized laser field and (b)–(f) in a two-color laser field with the Coulomb potential. The relative phases are $\phi =0,\pi /4,\pi /2,3\pi /4,\mathrm{and}\pi$ for (b)–(f), respectively. The white and red (gray) lines show one cycle of the laser field and vector potential in arbitrary units. The laser intensity is $1\times {10}^{14}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2, \alpha =0.3, \omega =0.057$, and $I_p^{}=0.5$.

Figure 3

The same as Fig. 2 but by the TDSE calculation.

Figure 4

(a) and (b) show the cutoff of the positive momentum and the negative momentum along the laser polarization with respect to the relative phase $\phi$ calculated by the classical scattering model (solid black line) and the QTMC model (dashed blue line), respectively.

Figure 5

The simulated angular distributions of the low-energy electrons with including the Coulomb potential at $\phi =0,\pi /4,\pi /2,3\pi /4,\mathrm{and}\pi$ by (a) TDSE calculations and (b) the QTMC model. (c) shows the simulated PADs without considering the Coulomb potential and the scattering effect by the QTMC model. All parameters used are the same as in Fig. 2. Note the scale is different from Fig. 2.

Figure 6

(a)–(h) show the ionization probability of the initial transverse momentum with respect to the tunneling phase of electrons for $P_1$ [(a)–(d)] and $P_2$ [(e)–(h)] structures in Fig. 5. The first column is $\phi =0$, and the second column is $\phi =\pi$. (a), (b), (e), and (f) have considered the Coulomb potential. (c), (d), (g), and (h) have neglected the Coulomb potential. $D$ and $R_{1\left(2\right)}$ stand for the direct electrons and rescattered electrons, respectively. $R$ and $L$ in the subscripts stand for electrons finally distributing on the right side ($p_z>0$) and the left side ($p_z<0$), respectively. The vertical black dashed lines show that the ionization time is earlier with considering the Coulomb potential than that without considering the Coulomb potential. A logarithmic scale has been used in the color bar to describe the ionization amplitude.