Theoretical study on the angular correlation of two Lyman-α photons generated by single-photon absorption of a hydrogen molecule

Abstract

The angular correlation of two Lyman-α photons generated by the linearly polarized single-photon absorption of H2(X 1Σg+) followed by the neutral dissociation of the doubly excited Q21Πu(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.

Effect of entanglement on the decay dynamics of a pair of H(2p) atoms due to spontaneous emission

“…More recently Jänkälä et al [11] formulated a general theoretical model to calculate the angular distribution of two fluorescence photons from entangled atomic fragments in the photodissociation of a diatomic molecule. They calculated the angular distribution of two Lyman-α photons in process (1), which shows a shape similar to that by Miyagi et al [9] but weaker anisotropy. In a paper subsequent to that of Miyagi et al [9], Tanabe et al [12] reported the experimental angular distribution of two Lyman-α photons in process (1) measured at the incident photon energy of 33.66 eV and at the hydrogen gas pressures of 0.40 and 0.13 Pa.…”

“…They calculated the angular distribution of two Lyman-α photons in process (1), which shows a shape similar to that by Miyagi et al [9] but weaker anisotropy. In a paper subsequent to that of Miyagi et al [9], Tanabe et al [12] reported the experimental angular distribution of two Lyman-α photons in process (1) measured at the incident photon energy of 33.66 eV and at the hydrogen gas pressures of 0.40 and 0.13 Pa. The results were compared with the theoretical prediction by Miyagi et al [9].…”

“…The entangled pair of H(2p) atoms in Eq. (2) emits an entangled pair of Lyman-α photons, i.e., the entanglement in the pair of H(2p) atoms is copied to the pair of Lyman-α photons, resulting in strong anisotropy in the angular distribution of two Lyman-α photons as calculated by Miyagi et al [9] (solid line in Fig. 2).…”

“…In a paper subsequent to that of Miyagi et al [9], Tanabe et al [12] reported the experimental angular distribution of two Lyman-α photons in process (1) measured at the incident photon energy of 33.66 eV and at the hydrogen gas pressures of 0.40 and 0.13 Pa. The results were compared with the theoretical prediction by Miyagi et al [9]. Tanabe et al [12] found that (i) the experimental angular distributions seem to approach the theoretical one with decreasing pressure, which indicates the generation of an entangled pair of H(2p) atoms expressed by Eq.…”

“…In the first paper, Miyagi et al [9] pointed out that a pair of H(2p 0 ) and H(2p ±1 ) atoms produced from an H 2 molecule in the 1 u state, where the lower subscripts of 0 and ±1 denote the magnetic quantum * odagiri.t.aa@m.titech.ac.jp numbers m with respect to the internuclear axis, is entangled as follows:…”