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Few-Body Systems

Ground-State Entanglement Properties of Helium Atom in a Finite Spherical Cavity

Przemysław Kościk, Jayanta K. Saha

Published May 19, 2015• 12 citations
Publisher

Abstract

The effects of the spatial confinement on the ground-state entanglement properties of the helium atom have been studied. The finite oscillator potential is used to represent the confining potential. The transition to the free atom regime and the harmonic confinement regime are discussed in detail in dependence of the control parameters of the system.

DOI
10.1007/s00601-015-1000-1

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The effects of the spatial confinement on the ground-state entanglement properties of the helium atom have been studied. The finite oscillator potential is used to represent the confining potential. The transition to the free atom regime and the harmonic confinement regime are discussed in detail in dependence of the control parameters of the system.
We explore ground-state entanglement properties of helium atom confined at the center of an impenetrable spherical cavity of varying radius by using explicitly correlated Hylleraas-type basis set. Results for the dependencies of the von Neumann and linear entanglement entropic measures on the cavity radius are discussed in details. Some highly accurate numerical results for the von Neumann and linear entropy are reported for the first time. It is found that the transition to the strong confinement regime is manifested by the entropies as an appearance of the inflection points on their variations.
The properties of the ground state of the hydrogen atom in a spherical vacuum cavity with general boundary “not going out” conditions (i.e., when the probability current through the boundary vanishes) are studied. It is shown that in contrast to the confinement of an atom by a potential barrier, in this case depending on the parameters of the cavity, the atom could be in stable equilibrium at the center of the cavity or shift towards its periphery: spontaneous breaking of spherical symmetry occurs. The phase diagram of the shift and the dependence of the shift value and the binding energy of the ground state of the atom on the cavity parameters are presented. At the same time, the deformation properties of the electron wave function (WF) for an asymmetric distortion are so nontrivial that a non-zero shift occurs even when an electron is repulsed from the cavity boundary.
The potential energy curve and the electron density distribution for low-lying electronic states of the helium and lithium atoms confined by an anisotropic harmonic oscillator potential have been studied for different confinement parameters (ω x , ω y , ω z ) by using the quantum chemical configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set supplemented by a quantum chemical standard Cartesian Gaussian basis set, respectively. In the case of the helium atom full CI wavefunctions have been used, and in the case of the lithium atom multi-reference CI wavefunctions have been employed. The results for the two confined quantum systems are compared to each other: parabolic-and non-parabolic-type potential energy curves are observed for states of both atoms in different type harmonic oscillator confinement. The non-parabolic potentials always appear in pairs, one with a double minimum and the other with a sharp edge at the minimum. They result from the interaction of energetically nearby states of the same symmetry. The electron density distributions of the states of the two atoms show deformation from spherical symmetry according to the symmetry and strength of the confining potential at the position of the atoms. The electron distribution of the states having non-parabolic potential energy curves is strongly deformed and occasionally shows curvilinear nodal planes of parabolic shape.
We study the time evolution of entangled states of a pair of identical atoms, considered in the harmonic approximation, coupled to an environment represented by an infinite set of free oscillators, with the whole system confined within a spherical cavity of radius RRR. Taking the center-of-mass and the relative-position coordinates, and using the dressed-state approach, we present the time evolution of some quantities measuring the entanglement for both limits of a very large and a small cavity; the chosen examples are simple and illustrate these very distinct behaviors.
In this work, we investigate several entropic and complexity measures, including the Shannon entropy, Fisher information, Tsallis entropy [Formula: see text] for [Formula: see text], and the disequilibrium D. In addition, we analyze the influence of the spherical confinement on the behavior of complexity measures, particularly, the Fisher–Shannon [Formula: see text] and López–Ruiz–Mancini–Calbet [Formula: see text] complexities. Within this framework, the ground state of the helium atom is studied under spherical confinement using the Variational Monte Carlo (VMC) method. One-electron expectation values of radial moments [Formula: see text] for [Formula: see text] as well as interelectronic moments [Formula: see text] over the same range of exponents are computed. The obtained results provide a detailed description of how information content, spatial distribution and structural complexity evolve as the confinement radius [Formula: see text] is varied, offering new insights into correlated confined quantum systems.
We provide benchmark values for Shannon information entropies in position space for the ground state and ls2s 1Se excited state of helium confined with finite confinement potentials by employing the highly correlated Hylleraas-type wave functions. For the excited state, a “tilt” (small oscillation) on the curve of Shannon entropy as a function of width size for the confinement potential is observed. Justified by the behavior of the electron density, the localization or delocalization of the helium wave functions confined with repulsive and attractive finite oscillator (FO) potentials are examined.