Large Pressure Effect on the Angular Distribution of Two Lyman-$\alpha$ Photons Emitted by an Entangled Pair of $\mathbf{H}(2p)$ Atoms in the Photodissociation of ${\mathbf{H}}_2$

The angular distribution of two Lyman-$\alpha$ photons, i.e., the probability density that two Lyman-$\alpha$ photons are emitted in given directions, in the photodissociation of a hydrogen molecule have been measured at the hydrogen gas pressures of 0.40 and 0.13 Pa. We have found that the experimental angular distributions seem to approach the theoretical one by our group [J. Phys. B 40, 617 (2007)] with decreasing pressure, which indicates the generation of the entangled pair of $\mathrm{H}(2p)$ atoms shown in the theory and the role of the reaction of the entangled pair of $\mathrm{H}(2p)$ atoms with an ${\mathrm{H}}_2$ molecule that efficiently changes the entanglement.

Figure 1

The calculated angular distribution of two Lyman-$\alpha$ photons in the photodissociation of ${\mathrm{H}}_2$ [5].

Figure 2

Angular distribution of two Lyman-$\alpha$ photons in the photodissociation of a hydrogen molecule under the relation of ${\Theta }_d={\Theta }_c+\pi$. □: experimental results at 33.66 eV incident photon energy and 0.40 Pa hydrogen gas pressure; ●: those at 0.13 Pa, solid line: theoretical angular distribution for the photon-pair state $|\psi ⟩$ in Eq. (3) [5]; dashed line: that for the photon-pair state $|{\gamma }_a{\varphi }_b⟩$ [5]; $+$: convoluted result of the solid line with the angular resolution. All the results are normalized to unity at ${\Theta }_c=-90°$.