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Physical Review A

Entangled pairs of 2p atoms produced in photodissociation of H2 and D2

Yutaro Torizuka, Kouichi Hosaka, Philipp Schmidt, Takeshi Odagiri, André Knie, Arno Ehresmann, 陵子 向後, M. Kitajima, Noriyuki Kouchi

Published Jun 25, 2019• 7 citations
Publisher

Abstract

The angular correlation functions (ACFs) of a pair of Lyman-$\ensuremath{\alpha}$ photons in photodissociation of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ 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 ${1}_{u}$ 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 ${1}_{u}$ symmetry properties, which are invariant during the dissociation from the Franck-Condon region towards infinite internuclear distance.

DOI
10.1103/physreva.99.063426

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The angular correlation functions (ACFs) of a pair of Lyman-\ensuremathα\ensuremath{\alpha}\ensuremathα photons in photodissociation of H2{\mathrm{H}}_{2}H2​ and D2{\mathrm{D}}_{2}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-\ensuremathα\ensuremath{\alpha}\ensuremathα photons and find out whether the atom pair is entangled or not. Searching for reasonable 2p2p2p atom-pair states that reproduce the experimental ACFs to solve the issue, we show that hydrogen molecules are photoexcited to the Q21\ensuremathΠu(1){Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)Q2​1\ensuremathΠu​(1) state in the Franck-Condon region and then the Q21\ensuremathΠu(1){Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)Q2​1\ensuremathΠu​(1) state comes to superpose with the Q23\ensuremathΣu+(2){Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}(2)Q2​3\ensuremathΣu+​(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 2p2p2p atom pairs turn out to be in the 1u{1}_{u}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{1}_{u}1u​ symmetry properties, which are invariant during the dissociation from the Franck-Condon region towards infinite internuclear distance.
An angular correlation function (ACF) of a pair of Lyman-$\ensuremath{\alpha}$ photons produced in photodissociation of H2{\mathrm{H}}_{2}H2​ with linearly polarized incident light is measured on a whole sphere at a 33.66-eV photon energy so that we may distinctly substantiate that the 2p2p2p atom pairs are in the state previously identified by Torizuka et al. as the 2p2p2p atom-pair state [Phys. Rev. A 99, 063426 (2019)], who measured the ACF only on a circle in the plane perpendicular to the incident light beam. The 2p2p2p atom-pair state determined with much less uncertainty than before is investigated in terms of whether or not the state is entangled. We discover that the pair of fragment H(2p)\mathrm{H}(2p)H(2p) atoms is certainly entangled in terms of the electron-electron entanglement, and obtain the entanglement entropy of the 2p2p2p atom-pair state. The similar discussion is made in terms of the electronic spatial-spin entanglement too, where the spatial motion and spin motion of electrons are considered nonidentical partial systems at variance with the former electron-electron entanglement. It turns out that the pair of fragment H(2p2p2p) atoms is entangled in terms of the electronic spatial-spin entanglement as well as the electron-electron 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 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.
In this paper, as a continuation of our recent article demonstrating that the 2p atom pair is entangled in the H2 photodissociation [Phys. Rev. A 111, 023116 (2025)], we have discovered the origins of the entanglement for the 2p atom-pair state and obtained the entanglement entropies by origins. The same investigation has been carried out for the precursor molecular state of the 2p atom pair. The reason for the increase of the entanglement entropy during the dissociation from the precursor molecule into the H(2p) + H(2p) atom pair has been made clear.
We have measured the coincidence time spectra of two Lyman-$\ensuremath{\alpha}$ photons emitted by a pair of H(2p2p2p) atoms in the photodissociation of H2{\text{H}}_{2}H2​ at the incident photon energy of 33.66 eV and at the hydrogen gas pressures of 0.40 and 0.02 Pa. The decay time constant at 0.02 Pa is approximately half the lifetime of a single H(2p2p2p) atom, 1.60 ns, while the decay time constant at 0.40 Pa is in agreement with the lifetime of a single H(2p2p2p) atom. It turns out that the decay faster than the lifetime of a single H(2p2p2p) atom originates from the entanglement in the pair of H(2p2p2p) atoms. We have demonstrated an effect of entanglement on atomic decay.