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Physical Review A

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

Takehiko Tanabe, Takeshi Odagiri, M. Nakano, Yoshiaki Kumagai, Isao Suzuki, M. Kitajima, Noriyuki Kouchi

Published Oct 20, 2010• 24 citations
Publisher

Abstract

We have measured the coincidence time spectra of two Lyman-$\ensuremath{\alpha}$ photons emitted by a pair of H($2p$) atoms in the photodissociation of ${\text{H}}_{2}$ 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($2p$) 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 turns out that the decay faster than the lifetime of a single H($2p$) atom originates from the entanglement in the pair of H($2p$) atoms. We have demonstrated an effect of entanglement on atomic decay.

DOI
10.1103/physreva.82.040101

Related papers

Dynamics of entangled H(2p) pair generated in the photodissociation of H2

Takeshi Odagiri, Takehiko Tanabe, Noriyuki Kouchi

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.

Journal of Physics Conference Series•Nov 5, 2012•5 citations

Large Pressure Effect on the Angular Distribution of Two Lyman- α Photons Emitted by an Entangled Pair of H(2p) Atoms in the Photodissociation of H2

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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.

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Reply to “Comment on ‘Effect of entanglement on the decay dynamics of a pair of H( 2p ) atoms due to spontaneous emission’ ”

Takehiko Tanabe, Takeshi Odagiri, M. Nakano +4 more

In this Reply to the preceding Comment by Sancho and Plaja, we point out the difference between the coincidence time spectrum of two Lyman-$\ensuremath{\alpha}$ photons measured by us and their theoretical one.

Physical Review A•Jun 13, 2011•3 citations

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

Pedro Sancho, Luis Plaja

T. Tanabe et al. [Phys. Rev. A 82, 040101(R) (2010)] have experimentally demonstrated that the emission properties of unstable atoms in entangled and product states are different. The authors define an apparent decay time as a fitting parameter which falls below the lifetime of the single atom for entangled pairs. We argue that their results about coincidence time spectra are correct, but those concerning lifetimes cannot be considered conclusive because they assume the emission of photons by the two atoms to be independent processes, a doubtful hypothesis for entangled states. We suggest an improved evaluation of the lifetimes based on a rigorous approach, which demands some modifications of the experimental procedure.

arXiv:1106.2667•Physical Review A•Jun 13, 2011•8 citations

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

Yutaro Torizuka, Kouichi Hosaka, Philipp Schmidt +6 more

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.

Physical Review A•Jun 25, 2019•7 citations

Absence of entanglement effect on the decay dynamics of H(2p) pairs produced by VUV photodissociation of H2

Xavier Urbain, Arnaud Dochain, Clément Lauzin +1 more

The effects of entanglement on the spontaneous decay of a pair of H(2 p ) previously observed by Tanabe et al. ( Phys. Rev. A 82 , 040101 (2010)) could not be reproduced despite careful determination of emission times with respect to the synchrotron bunch.

Journal of Physics Conference Series•Sep 7, 2015•5 citations
We have measured the coincidence time spectra of two Lyman-\ensuremathα\ensuremath{\alpha}\ensuremathα 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.
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.
T. Tanabe et al. [Phys. Rev. A 82, 040101(R) (2010)] have experimentally demonstrated that the emission properties of unstable atoms in entangled and product states are different. The authors define an apparent decay time as a fitting parameter which falls below the lifetime of the single atom for entangled pairs. We argue that their results about coincidence time spectra are correct, but those concerning lifetimes cannot be considered conclusive because they assume the emission of photons by the two atoms to be independent processes, a doubtful hypothesis for entangled states. We suggest an improved evaluation of the lifetimes based on a rigorous approach, which demands some modifications of the experimental procedure.
The angular correlation functions (ACFs) of a pair of Lyman-$\ensuremath{\alpha}$ 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-$\ensuremath{\alpha}$ 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 ${Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ 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 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.