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arXiv:1808.08171 · Physical Review A

Interference effects due to nuclear motion of the hydrogen molecule

Lívia O. Santos, Amanda Alencar, Ítalo Prazeres, François Impens, Jacques Robert, C. R. de Carvalho, N. V. de Castro Faria, Ginette Jalbert

Published Nov 28, 2018• 2 citations
arXivHTMLPDF

Abstract

We show that two-particle interferences can be used to probe the nuclear motion in a doubly excited hydrogen molecule. The dissociation of molecular hydrogen by electron impact involves several decay channels, associated with different molecular rotational states, which produce quantum interferences in the detection of the atomic fragments. Thanks to the correlations between the angular momentum and the vibrational states of the molecule, the fragments arising from each dissociation channel carry out a phase shift which is a signature of the molecule rotation. These phase shifts, which cannot be observed in a single-atom detection scheme, may be witnessed under realistic experimental conditions in a time-of-flight coincidence measurement. We analyze the interferences arising from the two lowest-energy rotational states of a parahydrogen molecule. Our result shows the relevance of two-fragment correlations to track the molecular rotation.

DOI
10.1103/physreva.98.052136

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We show that two-particle interferences can be used to probe the nuclear motion in a doubly excited hydrogen molecule. The dissociation of molecular hydrogen by electron impact involves several decay channels, associated with different molecular rotational states, which produce quantum interferences in the detection of the atomic fragments. Thanks to the correlations between the angular momentum and the vibrational states of the molecule, the fragments arising from each dissociation channel carry out a phase shift which is a signature of the molecule rotation. These phase shifts, which cannot be observed in a single-atom detection scheme, may be witnessed under realistic experimental conditions in a time-of-flight coincidence measurement. We analyze the interferences arising from the two lowest-energy rotational states of a parahydrogen molecule. Our result shows the relevance of two-fragment correlations to track the molecular rotation.
The dissociative electron transfer from He into 10 keV H2+ was measured in a kinematically complete experiment by using the cold target recoil ion momentum spectroscopy imaging technique in combination with a highly resolving molecular fragment imaging technique. The electron transfer into the dissociative b(3)Sigma+_(u) state of H2 could be selected by kinematic conditions. We find a striking double slit interference pattern in the transverse momentum transfer which we can modify by selecting different internuclear distances. Compared to an optical double slit, interference minima and maxima are interchanged. The latter is the result of a phase shift in the electronic part of the wave function.
We present a scheme well suited to investigate quantitatively the angular-momentum coherence of molecular fragments. Assuming that the dissociated molecule has a null total angular-momentum, we investigate the propagation of the corresponding atomic fragments in the apparatus. We show that the envisioned interferometer enables one to distinguish unambiguously a spin-coherent from a spin-incoherent dissociation, as well as to estimate the purity of the angular-momentum density matrix associated with the fragments. This setup, which may be seen as an atomic analogue of a twin-photon interferometer, can be used to investigate the suitability of molecule dissociation processes —such as the metastable hydrogen atoms H(2 2 S )-H(2 2 S ) dissociation— for coherent twin-atom optics.
It is a difficult task to obtain “twin atoms”, i.e. pairs of massive particles such that one can perform experiments in the same fashion that is routinely done with “twin photons”. One possible route to obtain such pairs is by dissociating homonuclear diatomic molecules. We address this possibility by investigating the production of metastable H(2s) atoms coming from the dissociation of cold H2 molecules produced in a Campargue nozzle beam crossing an electron beam from a high intensity pulsed electron gun. Dissociation by electron impact was chosen to avoid limitations of target molecular excited states due to selection rules. Detectors placed several centimeters away from the collision center, and aligned with respect to possible common molecular dissociation channel, analyze the neutral fragments as a function of their time-of-flight (TOF) through Lyman-α detection. Evidence for the first time observed coincidence of pairs of H(2s) atoms obtained this way is presented.
In photodissociation of a homonuclear diatomic molecule, conservation of linear and angular momenta requires that each atomic fragment follow identical but oppositely directed trajectories with respect to the molecular center of mass. For certain values of the incident photon energy, one of the atoms will be electronically excited while the other will be in its ground state. When a detector records the undispersed fluorescence from the decay of the excited atom it cannot distinguish which trajectory the excited atom followed and hence whether the photon possesses a blue or red Doppler shift corresponding to recoil towards or away from the detector. According to the principle of superposition in quantum mechanics, the wave function of the photon must be a sum over two paths corresponding to emission from an excited atom in either of the two recoil directions. Detection of such photons gives rise to an interference between the probability amplitudes for the two paths that is manifested in the output from the photodetector as a beat frequency. Since photodissociation of an ensemble of molecules gives rise to a distribution of recoil directions relative to the electric vector of the incident radiation, a range of beat frequencies must be present in the detected signal. This paper gives a calculation of expected output voltage waveforms from a photodetector viewing atomic fluorescence excited by molecular photodissociation. Expressions are given for partial Fourier transforms of the photodetector signals. The results show that the shape of the voltage waveforms depends strongly on the asymmetry parameter for recoil of the photofragments and on whether or not the magnetic sublevels of the excited atomic state are created in a coherent superposition.
ABSTRACT: In the present work, we have computed the entanglement between the electronic and nuclear motions in two molecular model systems: the one-dimensional hydrogen molecular ion (H2+) and the Shin-Metiu model, considering the molecules as a bipartite systems: electron and nuclear motion. For that purpose, we have computed the Born-Oppenheimer and non-Born-Oppenheimer (Born-Huang) wave function in terms of the Fourier Grid Hamiltonian basis that expands both the electronic and nuclear wave functions. Also, according to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, there is a much shorter but equivalent expansion in terms of the Schmidt bases for the electronic and nuclear sub-spaces. In these models of distinguishable coupled particles we have shown that the entanglements contents do not increase monotonically with the excitation energy. In the hydrogen molecular ion and in the ShinMetiu model, the entanglements contents for each Born-Oppenheimer electro-nuclear state is quantified through the von-Neumann and linear entropies and we have shown that entanglement serves as a witness of distinguishability of nuclear states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.
This work presents a comprehensive comparison of quantum-mechanical and classical evolution for nuclear motion within a finite-dimensional quantum chemistry model. We employ a modified Tavis–Cummings–Hubbard model featuring two two-level artificial atoms in optical cavities to simulate the association and dissociation of a neutral hydrogen molecule. The initial conditions leading to the formation and decomposition of the molecule are examined. Dissipation in a Markovian open system is simulated by solving the Lindblad master equation. We compare the quantum and classical descriptions of nuclear motion: quantum mobility is characterized by nuclear tunneling, while classical motion is represented via fluctuations in interaction strengths. The emergence of dark states during dissociation and their significant impact on the evolutionary outcome are also analyzed. Key findings show that classical motion reaches the same final molecular states as quantum tunneling but requires an order-of-magnitude shorter time, with distinct patterns of population evolution. Two singlet dark states are identified that modify the branching ratio between neutral and ionic products.