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arXiv:1011.2161 · The Journal of Chemical Physics

Excited electron-bubble states in superfluid 4He: A time-dependent density functional approach

David Mateo, Dafei Jin, M. Barranco, Martí Pi

Published Jan 24, 2011• 37 citations
arXivHTMLPDF

Abstract

We present a systematic study on the excited electron-bubble states in superfluid (4)He using a time-dependent density functional approach. For the evolution of the 1P bubble state, two different functionals accompanied with two different time-development schemes are used, namely an accurate finite-range functional for helium with an adiabatic approximation for electron versus an efficient zero-range functional for helium with a real-time evolution for electron. We make a detailed comparison between the quantitative results obtained from the two methods, which allow us to employ with confidence the optimal method for suitable problems. Based on this knowledge, we use the finite-range functional to calculate the time-resolved absorption spectrum of the 1P bubble, which in principle can be experimentally determined, and we use the zero-range functional to real-time evolve the 2P bubble for several hundreds of picoseconds, which is theoretically interesting due to the break down of adiabaticity for this state. Our results discard the physical realization of relaxed, metastable configurations above the 1P state.

DOI
10.1063/1.3544216

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We present a systematic study on the excited electron-bubble states in superfluid (4)He using a time-dependent density functional approach. For the evolution of the 1P bubble state, two different functionals accompanied with two different time-development schemes are used, namely an accurate finite-range functional for helium with an adiabatic approximation for electron versus an efficient zero-range functional for helium with a real-time evolution for electron. We make a detailed comparison between the quantitative results obtained from the two methods, which allow us to employ with confidence the optimal method for suitable problems. Based on this knowledge, we use the finite-range functional to calculate the time-resolved absorption spectrum of the 1P bubble, which in principle can be experimentally determined, and we use the zero-range functional to real-time evolve the 2P bubble for several hundreds of picoseconds, which is theoretically interesting due to the break down of adiabaticity for this state. Our results discard the physical realization of relaxed, metastable configurations above the 1P state.
A method for calculating hydrodynamic added mass within the framework of time-dependent bosonic density functional theory (DFT) for superfluid 4{}^{4}4He is developed. As a calibration of the model, it is shown to reproduce the classical hydrodynamic limit for purely repulsive interactions. To model real systems for which experimental data are available, the following ions were considered: Be+{}^{+}+, K+{}^{+}+, Ca+{}^{+}+, Sr+{}^{+}+, and Ba+{}^{+}+ cations as well as the F${}^{\ensuremath{-}}$, Cl${}^{\ensuremath{-}}$, I${}^{\ensuremath{-}}$, and Br${}^{\ensuremath{-}}$ anions. The DFT model requires the ion-helium pair potential data as input, which were obtained from electron structure calculations by employing coupled clusters theory. The resultant static liquid density profiles as calculated by DFT were found to be in good agreement with previously published quantum Monte Carlo data. The calculated added masses for the positive ions correlated directly with the experimentally observed ion mobility data, by which the ions could be separated into two different categories based on the degree of the first solvent shell following the ion. The calculated added masses for the negative ions were found to be in disagreement with the existing experimental data, suggesting the possibility that other negatively charged species were observed in previous experiments. The negatively charged ions are predicted to have mobilities ($\ensuremath{\mu}$) within the range 0.8--1.0 cm2{}^{2}2 V${}^{\ensuremath{-}1}$ s${}^{\ensuremath{-}1}$ in superfluid helium at 1.3 K with the order $\ensuremath{\mu}$(I${}^{\ensuremath{-}}$) >>> $\ensuremath{\mu}$(Br${}^{\ensuremath{-}}$) >>> $\ensuremath{\mu}$(Cl${}^{\ensuremath{-}}$) >>> $\ensuremath{\mu}$(F${}^{\ensuremath{-}}$).
The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.
The electron bubble in superfluid helium has two degrees of freedom that may offer exceptionally low dissipation: the electron's spin and the bubble's motion. If these degrees of freedom can be read out and controlled with sufficient sensitivity, they would provide a novel platform for realizing a range of quantum technologies and for exploring open questions in the physics of superfluid helium. Here we propose a practical scheme for accomplishing this by trapping an electron bubble inside a superfluid-filled opto-acoustic cavity.
\n\t\t\t\tA theoretical analysis of the line broadening of localized atomic transitions in liquid helium is presented. It is shown that accurate information can be derived on the long-range part of the He*-He interaction as well as on the local structure near the He* emitters. The analysis confirms that in corona discharges in liquid helium the emitting He* atoms reside in cavities and that for known He*-He interaction the size of the cavities can be deduced from the line profile. The He*-He interaction was calculated using the full configuration interaction (CI) method as implemented in the Molpro package. The widths of atomic lines due to fluorescent transitions between different excited states of helium atoms were calculated as a function of external pressure in the range from 0.1 and 3.5 MPa using the static approximation method, and the input from the results of the CI calculation and cavity diameters calculated using the bubble model. The calculated widths showed excellent agreement with experimental data of liquid helium excited by corona discharges. A second, analytical analysis using a power function to represent the He*-He interaction showed qualitative agreement with the experimental data.\n\t\t\t
Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the \boldsymbol{GW} 𝐆 𝐖 approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.
Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density-functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approximation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods.