Tuning of Efimov states in non-integer dimensions
- URL: http://arxiv.org/abs/2303.03845v1
- Date: Tue, 7 Mar 2023 12:20:47 GMT
- Title: Tuning of Efimov states in non-integer dimensions
- Authors: E. Garrido and A.S. Jensen
- Abstract summary: We show that by combining Feshbach resonances with external confining potentials, the energy scale factor of neighboring Efimov states can be greatly reduced.
The results are universal as they only rely on large-distance properties.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The purpose of this paper is to show that, by combining Feshbach resonances
with external confining potentials, the energy scale factor of neighboring
Efimov states can be tremendously reduced. The Efimov conditions can be reached
for systems made of three different particles. For the case of two identical
light particles and a heavy particle the energy factor can be reduced by many
orders of magnitude, and the Efimov states are in this way more easily
reachable experimentally. The equivalence between external potentials and the
formulation in terms of non-integer dimensions, $d$, is exploited. The
technically simpler $d$-method is used to derive analytic expressions for
two-component relative wave functions describing two short-range square-well
interacting particles. The two components express one open and one closed
channel. The scattering length is obtained after phase shift expansion,
providing an analytic form for the Efimov condition. We illustrate the results
by means of systems made of $^7$Li, $^{39}$K, and $^{87}$Rb, with realistic
parameters. The related pairs of dimension and magnetic field are shown and
discussed. The results are universal as they only rely on large-distance
properties.
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