Angle-dependent electron-electron correlation in the single ionization of H2 in strong laser fields

Abstract

The one-photon ionization and tunneling ionization of H₂ exposed to strong XUV and infrared laser pulses are studied by numerically simulating the four-dimensional time-dependent Schrödinger equation, which includes two-electron dynamics for arbitrary angle between the molecular axis and the laser polarization direction. In the one-photon single ionization of H₂, one electron escapes fast and the other bound electron is not disturbed but remains in coherent superposition of two electronic states of [Formula: see text]. In another case, under the irradiation of strong infrared laser pulses, one electron tunnels through the laser-dressed Coulomb barrier, and the other bound electron has enough time to adapt to the potential of [Formula: see text] and thus is prone to transfer to the ground electronic state of [Formula: see text]. In the intermediate regime, between the one photon and tunneling regimes, this electron-electron correlation depends strongly on the laser frequency, laser intensity and on the angle between laser polarization and the molecular axis.

Figure 1

Electron probability distributions obtained by projecting the four-dimensional wave function of H₂ onto two-dimensional wave function of ${\mathrm{H}}_2^{+}$ in (a) 1sσ_g state and (b) 2pσ_u state, according to Eq. 9. The internuclear distance R is 5 a.u. (c) Probabilities of $W_{1s{\sigma }_g}$, $W_{2p{\sigma }_u}$, and (d) The ratio of $W_{2p{\sigma }_u}/W_{1s{\sigma }_g}$ as a function of the internuclear distance.

Figure 2

Singly ionized photoelectron momentum distributions at different laser polarization directions of TDSE results governed by Eq. 9 in the top row and SFA results governed by Eq. 6 in the bottom row. (a,c) For ${\mathrm{H}}_2^{+}$ in the 1sσ_g state after single ionization. (d,e and f) For ${\mathrm{H}}_2^{+}$ in the 2pσ_u state. The lower row represents corresponding results of SFA. All the calculations were carried out with ω = 2.28 a.u. and R = 5 a.u.

Figure 3

The θ-dependent single ionization probability (left column), ionization probabilities associated with the ground ionic state $W_{1s{\sigma }_g}$ (middle column, crosses) and the first excited ionic state $W_{2p{\sigma }_u}$ (middle column, diamonds), and the ratio of $W_{2p{\sigma }_u}/W_{1s{\sigma }_g}$ (right column). The three rows from up to bottom are for the internuclear distances R = 1.67, 3.5 and 5 a.u., respectively. For better clarity, The probabilities of $W_{2p{\sigma }_u}$ in (b) and (e) have been multiplied by 100 and 8, respectively. All the calculations were carried out with photon energy ω = 2.28 a.u.

Figure 4

(a) The final probabilities of the first two states as a function of the photon energy. The solid and dashed lines represent excitations at polarization angle θ = 0 and π/2, respectively. The laser intensity I₀ is 10¹⁴ W/cm². (b) Ratios with crosses were obtained by probabilities of solid blue and solid black lines in (a), and the black solid line represents ratios of laser field intensity at 3 × 10¹⁴ W/cm². All the calculations were carried out with internuclear distance R = 5 a.u.

Figure 5

Probability distributions of the bound electron in space (the left and middle columns) and momentum (the right column) representations at polarization angles θ = 0 (upper panels) and θ = π/2 (lower panels). (a and d) For wave function at t = 50 a.u., (b and e) for wave function at t = 85 a.u. (c and f) are the momentum distributions of (b and e), respectively. The photon energy is 0.057 a.u. and I₀ = 2 × 10¹⁴ W/cm². The calculations were carried out with internuclear distance R = 5 a.u.

Figure 6

(a) Branching ratios as a function of laser field intensity. The black line represents results with 4D H₂ model at R = 5 a.u. and ω = 0.114 a.u., the red line is the same with black line except that each electron has only one dimension (2D TDSE). The blue and green lines were obtained by the 2D model for R = 3.5 a.u., at ω = 0.114 and 0.076 a.u., respectively. (b) Branching ratios as a function of laser field wavelength. Other parameters are labeled.