arXiv:1803.05333 · Physical Review A

Observability of the Efimov spectrum in an electron-atom-atom system

Hui-Li Han, Chris H. Greene

Published Aug 30, 2018• 2 citations

Abstract

The bound states of a system consisting of two heavy identical atoms and one light electron interacting through finite-range pairwise potentials are explored, focusing on their dependence on the electron-atom scattering length. In the case of an exact resonance in the electron-atom interaction, the binding energy of an electron yields an effective $1/{r}^{2}$ potential for the relative motion of the atoms. One major finding is a universal potential that depends on the polarization length, which goes beyond the Efimov region. An analytic expression for that potential is extracted from numerical calculations. The spectrum of the $e+\mathrm{Rb}+\mathrm{Rb}$ system produced by the electron-atom polarization interaction exhibits three main sections: a nonuniversal transition region, a quasi-Efimov region, and a densely packed Efimov region.

DOI: 10.1103/physreva.98.023632

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arXiv:1803.05333 · Physical Review A

Observability of the Efimov spectrum in an electron-atom-atom system

Hui-Li Han, Chris H. Greene

Published Aug 30, 2018• 2 citations

arXiv HTML PDF

Abstract

1/{r}^{2}

potential for the relative motion of the atoms. One major finding is a universal potential that depends on the polarization length, which goes beyond the Efimov region. An analytic expression for that potential is extracted from numerical calculations. The spectrum of the

e+\mathrm{Rb}+\mathrm{Rb}

system produced by the electron-atom polarization interaction exhibits three main sections: a nonuniversal transition region, a quasi-Efimov region, and a densely packed Efimov region.

DOI: 10.1103/physreva.98.023632

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In systems of ultracold atoms, the quantum Efimov effect can appear where identical bosons form an infinite tower of bound trimer states in the resonant limit, at the bound dimer dissociation threshold. The most characteristic feature of this effect is that their energy spectrum obey a geometric scaling law, which is universal in the sense that it emerges irrespective of the nature of the two body forces. Using a model potential, constructed to resemble the two body interaction between alkali atoms, which was fine tuned to control the scattering length, energy eigenvalues for the two- and threebody problem were calculated numerically. The results where fitted to the analytic theory and the appearance of the first Efimov state was positioned at a scattering length of -9.23rvdW , which is in good agreement with the universal value -9.2rvdW .In systems of ultracold atoms, the quantum Efimov effect can appear where identical bosons form an infinite tower of bound trimer states in the resonant limit, at the bound dimer dissociation threshold. The most characteristic feature of this effect is that their energy spectrum obey a geometric scaling law, which is universal in the sense that it emerges irrespective of the nature of the two body forces. Using a model potential, constructed to resemble the two body interaction between alkali atoms, which was fine tuned to control the scattering length, energy eigenvalues for the two- and threebody problem were calculated numerically. The results where fitted to the analytic theory and the appearance of the first Efimov state was positioned at a scattering length of -9.23rvdW , which is in good agreement with the universal value -9.2rvdW .

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Analytical solution of the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials: Universal three-body parameter of mixed-dimensional Efimov statesAnalytical solution of the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials: Universal three-body parameter of mixed-dimensional Efimov states

Yuki Ohishi, Kazuki Oi, Shimpei Endo

We study the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials. Using the quantum defect theory, we obtain analytical solutions for both repulsive and attractive $1/r^3$ interactions. The obtained discrete-scale-invariant energies and wave functions, validated by excellent agreement with numerical results, provide a natural framework for describing the universality of Efimov states in mixed dimension. Specifically, we consider a three-body system consisting of two heavy particles with large dipole moments confined to a quasi-one-dimensional geometry and resonantly interacting with an unconfined light particle. With the Born-Oppenheimer approximation, this system is effectively reduced to the Schrödinger equation with $1/r^3$ and $1/r^2$ potentials, and manifests the Efimov effect. Our analytical solution suggests that, for repulsive dipole interactions, the three-body parameter of the mixed-dimensional Efimov states is universally set by the dipolar length scale, whereas for attractive interactions it explicitly depends on the short-range phase. We also investigate the effects of finite transverse confinement and find that our analytical results are useful for describing the Efimov states composed of two polar molecules and a light atom.We study the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials. Using the quantum defect theory, we obtain analytical solutions for both repulsive and attractive $1/r^3$ interactions. The obtained discrete-scale-invariant energies and wave functions, validated by excellent agreement with numerical results, provide a natural framework for describing the universality of Efimov states in mixed dimension. Specifically, we consider a three-body system consisting of two heavy particles with large dipole moments confined to a quasi-one-dimensional geometry and resonantly interacting with an unconfined light particle. With the Born-Oppenheimer approximation, this system is effectively reduced to the Schrödinger equation with $1/r^3$ and $1/r^2$ potentials, and manifests the Efimov effect. Our analytical solution suggests that, for repulsive dipole interactions, the three-body parameter of the mixed-dimensional Efimov states is universally set by the dipolar length scale, whereas for attractive interactions it explicitly depends on the short-range phase. We also investigate the effects of finite transverse confinement and find that our analytical results are useful for describing the Efimov states composed of two polar molecules and a light atom.

cond-mat.quant-gasCross-listedarXiv:2601.19517Physical Review ResearchJan 28, 20261 citation

1/{r}^{2}

e+\mathrm{Rb}+\mathrm{Rb}

system produced by the electron-atom polarization interaction exhibits three main sections: a nonuniversal transition region, a quasi-Efimov region, and a densely packed Efimov region.

{\mathcal{R}}_{{n}^{*}}{k}_{{n}^{*}}=\sqrt{(1+{s}_{0}^{2})/3}

derived with zero-range approximation. It is found that for the Efimov states that have large scaled sizes, their size-binding momentum relations follow the universal formula well. Our calculations demonstrate that size is an important characteristic in determining the universalities of Efimov states.

Analytical solution of the Schrödinger equation with

1/r^3

and attractive

1/r^2

potentials: Universal three-body parameter of mixed-dimensional Efimov states

We study the Schrödinger equation with

1/r^3

and attractive

1/r^2

potentials. Using the quantum defect theory, we obtain analytical solutions for both repulsive and attractive

1/r^3

interactions. The obtained discrete-scale-invariant energies and wave functions, validated by excellent agreement with numerical results, provide a natural framework for describing the universality of Efimov states in mixed dimension. Specifically, we consider a three-body system consisting of two heavy particles with large dipole moments confined to a quasi-one-dimensional geometry and resonantly interacting with an unconfined light particle. With the Born-Oppenheimer approximation, this system is effectively reduced to the Schrödinger equation with

1/r^3

and

1/r^2

potentials, and manifests the Efimov effect. Our analytical solution suggests that, for repulsive dipole interactions, the three-body parameter of the mixed-dimensional Efimov states is universally set by the dipolar length scale, whereas for attractive interactions it explicitly depends on the short-range phase. We also investigate the effects of finite transverse confinement and find that our analytical results are useful for describing the Efimov states composed of two polar molecules and a light atom.