We have measured the coincidence time spectra of two Lyman-α photons emitted by a pair of H(2p) atoms in the photodissociation of H 2 at the incident photon energy of 33.66 eV and at the hydrogen gas pressures of 0.40 Pa and 0.02 Pa, from which the angular distributions of two Lyman-α photons have been obtained. The experimental angular distributions indicate the generation of the entangled pair of H(2p) atoms as predicted by the theory of our group (Miyagi et al 2007 J. Phys. B 40 617) and the role of a new kind of reaction, i.e. the reaction of the entangled pair of H(2p) atoms with an H 2 molecule that efficiently changes the entanglement. It has turned out that more entangled pairs of H(2p) atoms survive at 0.02 Pa than at 0.40 Pa. The decay time constant in the coincidence time spectrum at 0.02 Pa is approximately half the lifetime of a single H(2p) atom, 1.60 ns, while the decay time constant at 0.40 Pa is in agreement with the lifetime of a single H(2p) atom. It follows that the decay faster than the lifetime of a single H(2p) atom originates from the entanglement in the pair of H(2p) atoms.
The angular correlation functions (ACFs) of a pair of Lyman-\ensuremath{\alpha} photons emitted from H fragments in the photodissociation of a hydrogen molecule are measured at a 33.66-eV incident photon energy and at hydrogen gas pressures of approximately 0.1 and 1 Pa. The ACFs are measured for both opposite and nonopposite arrangements of the two photon detectors. It turns out that the experimental ACFs involve neither the contribution of the reactions
H(n=2)+H2 nor the contribution of the cascade from
H(n \ensuremath{\geqslant} 3) to H(
2p) fragments. Thus the experimental ACFs are those for primary H(
2p) pairs following the photodissociation of
H2. The experimental ACFs are compared with (i) the theoretical ACF for entangled pairs of H(
2p) atoms, where the magnetic quantum number of each hydrogen atom is indefinite, and (ii) the theoretical ACF for H(
2p) pairs with definite magnetic quantum number of each hydrogen atom relative to the internuclear axis [the former entangled state of H(
2p) pairs is a sum of the latter pair states with definite magnetic quantum number]. In the theoretical ACF in (ii), the disentanglement in H(
2p) pairs during the dissociation is considered. The experimental ACFs show a similar tendency in angular dependence to the theoretical ACF for entangled H(
2p) pairs. However, there still remains a considerable difference in the variation magnitude between those experimental and theoretical ACFs. The experimental ACFs show the reverse tendency in angular dependence to the theoretical ACF for H(
2p) pairs with definite magnetic quantum number of each hydrogen atom relative to the internuclear axis. We thus conclude that the pair of H(
2p) atoms in the photodissociation of
H2 is unlikely to be in the definite states of magnetic quantum number of each hydrogen atom relative to the internuclear axis, i.e., unlikely to be in the components of the entangled state of H(
2p) pairs.
The angular correlation functions (ACFs) of a pair of Lyman-$\ensuremath{\alpha}$ photons in photodissociation of
H2 and
D2 are measured with linearly polarized incident light at a 33.66-eV incident photon energy in a wider angular range at a narrower angular step with smaller distortion than before [Y. Nakanishi et al., Phys. Rev. A 90, 043405 (2014)] so that we identify the atom-pair state emitting the pair of Lyman-$\ensuremath{\alpha}$ photons and find out whether the atom pair is entangled or not. Searching for reasonable
2p atom-pair states that reproduce the experimental ACFs to solve the issue, we show that hydrogen molecules are photoexcited to the ${Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state in the Franck-Condon region and then the ${Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state comes to superpose with the ${Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}(2)$ state as the internuclear distance increases to infinity. The superposition is brought about by the spin-orbit coupling, which is effective around infinite internuclear distance because the potential-energy curves of those states are close to each other, but is negligibly small around the Franck-Condon region because they are apart from each other. The
2p atom pairs turn out to be in the
1u superposition state, which is entangled. We therefore conclude that an entangled pair of hydrogen atoms is spontaneously produced through the photodissociation of a hydrogen molecule, and the entanglement originates from the
1u symmetry properties, which are invariant during the dissociation from the Franck-Condon region towards infinite internuclear distance.
The angular correlation of two Lyman-α photons generated by the linearly polarized single-photon absorption of H 2 (X 1 Σ g + ) followed by the neutral dissociation of the doubly excited Q 2 1 Π u (1) state has been theoretically investigated with the second-order correlation function in quantum optics. A strong angular correlation has been obtained even for the molecules randomly oriented in space, due to the complicated entanglement of two H(2p) atoms in the intermediate state. It has been revealed how the symmetry properties in the electronic state are transferred to the two-photon state and how they manifest themselves in the angular correlation function.