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 H(2p) atoms shown in the theory and the role of the reaction of the entangled pair of H(2p) atoms with an H2 molecule that efficiently changes the entanglement.
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 paper describes the theoretical formulation of dissociative γ → 2γ scattering in fixed-in-space and randomly oriented diatomic molecules in the dipole approximation for excitation and 2γ production.Based on perturbation theory the double-differential cross section and the two-photon angular correlation function of the process is derived.The developed theory is applied to study the angular correlation function of the two Lyman-α photons produced via decay of the doubly excited Q 2 1 u (1) state of the H 2 molecule.
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.
An analytical expression of the angular correlation function of a pair of Lyman-$\ensuremath{\alpha}$ photons in the photodissociation of a hydrogen molecule is derived theoretically in a manner based on both atomic and molecular physics and quantum optics. The angular correlation function turns out to be expressed in terms of cosine (sine) functions of four angular variables of detectors with five coefficients. The angular correlation function is expanded in terms of the spherical harmonics for investigating which terms are involved, and we discuss the reason why they are involved. Interesting features are revealed in the expansion. We then search for a special detector arrangement where the angular-dependent terms vanish in the angular correlation function expressed in terms of the spherical harmonics. It turns out that no such detector arrangement in fact exists, but there is a special pair of detector arrangements where the angular-dependent terms vanish in the summation of two values of the angular correlation function expressed in terms of the spherical harmonics. We refer to such a pair of detector arrangements as a magic pair.