Laser-induced electron diffraction in ${\text{H}}_2$ with linear and circular polarization ultrashort XUV laser pulses

Numerical solution of the time-dependent Schrödinger equation for a two-dimension model of ${\text{H}}_2$ ionization by intense ultrashort (few cycles) extreme ultraviolet (XUV) laser pulses are presented to compare linear and circular polarization angular distributions for aligned molecules. Both ground $\left(X{{}^1\Sigma }_g^{+}\right)$ and excited $\left(A{{}^3\Sigma }_u^{+}\right)$ states ionization is calculated at equilibrium and for extended large internuclear distance configurations to study the effect of electron delocalization via molecular orbitals vs electron localization in Heitler-London atomic wave functions. It is found that at large distance for ionized electron wavelengths less than the internuclear distance, circular polarization ionization angular distributions exhibit signature of the entanglement of electrons by exchange, thus, allowing for a measure of exchange entanglement.

Figure 1

(Color online) Ionization angular distributions in ${\text{H}}_2$ electronic states at photon wavelength $\lambda =10\text{nm}$ and intensity $I_0=5.0\times {10}^{13}\text{W}/{\text{cm}}^2$ at equilibrium distance $R_e=1.675\text{a}\text{.u}\text{.}$. (a) $X{{}^1\Sigma }_g^{+}$, (b) $A{{}^3\Sigma }_u^{+}$. Solid black line (—): circular polarization; dashed green line (- -): parallel linear polarization; and dotted red line $(\cdots )$: perpendicular linear polarization. The corresponding wavelengths ${\lambda }_e$ of the ejected electron for the two electronic states are, respectively, 2.75 and 2.58 a.u. The units of angular distribution are arbitrary.

Figure 2

(Color online) Same as Fig. 1, except for photon wavelength $\lambda =5\text{nm}$. The wavelengths ${\lambda }_e$ for the two electronic states are, respectively, 1.65 and 1.62 a.u.

Figure 3

(Color online) Same as Fig. 1, except for nuclear distance $R=10\text{a}\text{.u}\text{.}$. Both wavelengths ${\lambda }_e$ of the ejected electron for the two electronic states are 2.44 a.u.