Entanglement and coherence in photoionization of H2 by an ultrashort XUV laser pulse

We make a theoretical investigation of photoionization of an ${\mathrm{H}}_{2}$ molecule, induced by the irradiation of an ultrashort extreme ultraviolet (XUV) laser pulse. We consider a system composed of a photoelectron ejected from ${\mathrm{H}}_{2}$ and the resultant ${{\mathrm{H}}_{2}}^{+}$ as a bipartite system. In order to clarify how the interparticle correlations among two electrons and two protons in ${\mathrm{H}}_{2}$ are reflected to the bipartite system, we examine the entanglement between the photoelectron and the vibrational states of ${{\mathrm{H}}_{2}}^{+}$ as well as the coherence in the vibrational states of ${{\mathrm{H}}_{2}}^{+}$ by simulating the photoionization process of one-dimensional ${\mathrm{H}}_{2}$. In the simulation, we solve a time-dependent Schr\"odinger equation using a symmetry-adapted grid method. On the basis of the simulations with ten different sets of three parameters characterizing an ultrashort XUV laser pulse, i.e., the pulse duration, the wavelength, and the peak intensity, we show that the extent of the entanglement depends sensitively on the coherence in the vibrational states of ${{\mathrm{H}}_{2}}^{+}$.