Nonsequential double ionization of helium in IR+XUV two-color laser fields: Collision-ionization process

We investigate the nonsequential double ionization (NSDI) process of an atom in IR+XUV two-color intense laser fields, where the photon energy of the XUV laser is higher than the atomic ionization threshold. By using the frequency-domain theory, we consider the NSDI as a process caused by the collision-ionization mechanism and obtain the NSDI spectrum that presents a multiplateau structure. With the help of channel analysis, we find that the height of a plateau in the NSDI spectrum is determined by the number of XUV photons absorbed by the electrons. Furthermore, to explain the interference structure in the NSDI spectrum, we also compare the contributions of forward and backward collisions to the NSDI probability. We find that the forward collision dominates the contributions to the NSDI when two electrons are ejected along the same direction and both forward and backward collisions make a comparable contribution to NSDI when the two electrons are ejected along opposite directions. By applying the saddle-point approximation, we obtain an energy-circle formula, which may illustrate the formation of the NSDI spectrum structure.

Figure 1

The NSDI momentum spectra of two ionized electrons with their momenta parallel to the lasers polarization direction (on a logarithmic scale).

Figure 2

The NSDI momentum spectra of the atom absorbing (a1) and (b1) zero, (a2) and (b2) one, and (a3) and (b3) two XUV photons in the ATI process (on a logarithmic scale).

Figure 3

Channel contributions of the NSDI momentum spectra of two ionized electrons with their momenta along the same direction for (a) $(1,-1)$, (b) $(1,0)$, (c) $(1,1)$, and (d) $(1,2)$ (on a logarithmic scale).

Figure 4

Channel contributions of the NSDI momentum spectra of two ionized electrons with their momenta along the opposite directions for (a) $(1,-1)$, (b) $(1,0)$, (c) $(1,1)$, and (d) $(1,2)$ (on a logarithmic scale).

Figure 5

Channel contributions of the NSDI momentum spectra of two ionized electrons with their momenta along the same direction for SSCs (a) $\left(1\right|-20,0)$, (b) $\left(1\right|0,0)$, (c) $\left(1\right|20,0)$, and (d) $\left(1\right|40,0)$. Also shown are the NSDI momentum spectra of the forward collision for SSCs (e) $\left(1\right|-20,0)$, (f) $\left(1\right|0,0)$, (g) $\left(1\right|20,0)$, and (h) $\left(1\right|40,0)$ and the NSDI momentum spectra of the backward collision for SSCs (i) $\left(1\right|-20,0)$, (j) $\left(1\right|0,0)$, (k) $\left(1\right|20,0)$, and (l) $\left(1\right|40,0)$ (on a logarithmic scale).

Figure 6

Channel contributions of the NSDI momentum spectra of two ionized electrons with their momenta along the same direction for SSCs (a) $\left(1\right|-20,1)$, (b) $\left(1\right|-10,1)$, (c) $\left(1\right|0,1)$, and (d) $\left(1\right|10,1)$. Also shown are the NSDI momentum spectra of the forward collision for SSCs (e) $\left(1\right|-20,1)$, (f) $\left(1\right|-10,1)$, (g) $\left(1\right|0,1)$, and (h) $\left(1\right|10,1)$ and the NSDI momentum spectra of the backward collision for SSCs (i) $\left(1\right|-20,1)$, (j) $\left(1\right|-10,1)$, (k) $\left(1\right|0,1)$, and (l) $\left(1\right|10,1)$ (on a logarithmic scale).

Figure 7

Channel contributions of the NSDI momentum spectra of two ionized electrons with their momenta along the opposite directions for SSCs (a) $\left(1\right|-20,0)$, (b) $\left(1\right|0,0)$, (c) $\left(1\right|20,0)$, and (d) $\left(1\right|40,0)$. Also shown are the NSDI momentum spectra of the forward collision for SSCs (e) $\left(1\right|-20,0)$, (f) $\left(1\right|0,0)$, (g) $\left(1\right|20,0)$, and (h) $\left(1\right|40,0)$ and the NSDI momentum spectra of the backward collision for SSCs (i) $\left(1\right|-20,0)$, (j) $\left(1\right|0,0)$, (k) $\left(1\right|20,0)$, and (l) $\left(1\right|40,0)$ (on a logarithmic scale).

Figure 8

Channel contributions of the NSDI momentum spectra of two ionized electrons with their momenta along the opposite directions for SSCs (a) $\left(1\right|-20,1)$, (b) $\left(1\right|-10,1)$, (c) $\left(1\right|0,1)$, and (d) $\left(1\right|10,1)$. Also shown are the NSDI momentum spectra of the forward collision for SSCs (e) $\left(1\right|-20,1)$, (f) $\left(1\right|-10,1)$, (g) $\left(1\right|0,1)$, and (h) $\left(1\right|10,1)$ and the NSDI momentum spectra of the backward collision for SSCs (i) $\left(1\right|-20,1)$, (j) $\left(1\right|-10,1)$, (k) $\left(1\right|0,1)$, and (l) $\left(1\right|10,1)$ (on a logarithmic scale).

Figure 9

The SSC $\left(1\right|s_1,0)$ spectra with $s_1=0$ and the corresponding energy circles at different collision moment $t_c=cos\left({\omega }_1{t}_0\right)$ determined by Eq. (19) for ${\mathbf{p}}^{\prime }$ along the same direction of the laser's electric polarization, which indicates that (b) and (d) are forward collisions and (a) and (c) are backward collisions (on a logarithmic scale).

Figure 10

The SSC $\left(1\right|s_1,0)$ spectra with $s_1=0$ and the corresponding energy circles at different collision moment $t_c=cos\left({\omega }_1{t}_0\right)$ determined by Eq. (19) for ${\mathbf{p}}^{\prime }$ along the opposite direction of the laser's electric polarization, which indicates that (b) and (d) are backward collisions and (a) and (c) are forward collisions (on a logarithmic scale).

Figure 11

The SSC $\left(1\right|s_1,1)$ spectra with $s_1=0$ and the corresponding energy circles at different collision moment $t_c=cos\left({\omega }_1{t}_0\right)$ determined by Eq. (19) for ${\mathbf{p}}^{\prime }$ along the same direction of the laser's electric polarization, which indicates that (b) and (d) are forward collisions and (a) and (c) are backward collisions (on a logarithmic scale).

Figure 12

The SSC $\left(1\right|s_1,1)$ spectra with $s_1=0$ and the corresponding energy circles at different collision moment $t_c=cos\left({\omega }_1{t}_0\right)$ determined by Eq. (19) for ${\mathbf{p}}^{\prime }$ along the opposite direction of the laser's electric polarization, which indicates that (b) and (d) are backward collisions and (a) and (c) are forward collisions (on a logarithmic scale).

Figure 13

Interference pattern on the NSDI momentum distributions of SSC $\left(1\right|20,0)$ for the forward collision of two ionized electrons with their momenta along (a) the opposite directions and (b) the same direction. The closed squares are the locations of destructive interference determined by $cos[f\left(t_0\right)-\pi /4]=0$ in Eq. (17) (on a logarithmic scale).

Figure 14

Interference pattern on the NSDI momentum distributions of SSC $\left(1\right|-10,1)$ for the forward collision of two ionized electrons with their momenta along (a) the opposite directions and (b) the same direction. The closed squares are the locations of destructive interference determined by $cos[f\left(t_0\right)-\pi /4]=0$ in Eq. (17) (on a logarithmic scale).