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arXiv:2106.01458 · Physical Review C

Efimov resonances above four-boson threshold

Arnoldas Deltuva

Published Jun 11, 2021• 1 citation
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Abstract

Four-boson Efimov physics is well known in the negative energy regime but far less above the four-body breakup threshold. The part of this region with negative two-boson scattering length is studied solving rigorous four-particle scattering equations for transition operators in the momentum space. Moving away from the unitary limit, the Efimov tetramers evolve from unstable bound states into resonances. Their energies and widths are studied as functions of the two-boson scattering length; a universal behavior is established and given in a dimensionless representation. The Efimov tetramers have finite width in the whole regime; they broaden rapidly in the resonance regime but remain narrower than the associated trimer. The resonant behavior is most clearly seen in the four-particle recombination rate.

DOI
10.1103/physrevc.103.064001

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Four-boson Efimov physics is well known in the negative energy regime but far less above the four-body breakup threshold. The part of this region with negative two-boson scattering length is studied solving rigorous four-particle scattering equations for transition operators in the momentum space. Moving away from the unitary limit, the Efimov tetramers evolve from unstable bound states into resonances. Their energies and widths are studied as functions of the two-boson scattering length; a universal behavior is established and given in a dimensionless representation. The Efimov tetramers have finite width in the whole regime; they broaden rapidly in the resonance regime but remain narrower than the associated trimer. The resonant behavior is most clearly seen in the four-particle recombination rate.
Three-boson Efimov physics is well known in the bound-state regime, but far less in the three-particle continuum at negative two-particle scattering length where Efimov states evolve into resonances. They are studied solving rigorous three-particle scattering equations for transition operators in the momentum space. The dependence of the three-boson resonance energy and width on the two-boson scattering length is studied with several force models. The universal limit is determined numerically considering highly excited states; simple parametrizations for the resonance energy and width in terms of the scattering length are established. Decreasing the attraction, the resonances rise not much above the threshold but broaden rapidly and become physically unobservable, evolving into subthreshold resonances. Finite-range effects are studied and related to those in the bound-state regime.
The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited Nth tetramer energy B(N)4 is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B4(N)/B3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.
We use exact four-boson scattering equations in the momentum-space framework to study the universal properties of shallow Efimov tetramers and their dependence on the two-boson scattering length. We demonstrate that, in contrast to previous predictions, the shallow tetramer in a particular experimentally unexplored regime is not an unstable bound state but an inelastic virtual state. This leads to a resonant behaviour of the atom-trimer scattering length and thereby to a resonant enhancement of the trimer relaxation in ultracold atom-trimer mixtures.