Tuning of Efimov states in non-integer dimensions

Abstract The purpose of this paper is to show that, by combining Feshbach resonances with external confining potentials, the energy scale factor neighboring Efimov states can be tremendously reduced. conditions reached for systems made three different particles. For case two identical light particles and a heavy particle, reduced many orders magnitude, are in way more easily reachable experimentally. equivalence between potentials formulation terms non-integer dimensions, d , exploited. technically simpler -method used derive analytic expressions two-component relative wave functions describing short-range square-well interacting components express one open closed channel. scattering length obtained after phase shift expansion, providing an form condition. We illustrate results means $$^7$$ 7 Li, $$^{39}$$ 39 K, $$^{87}$$ 87 Rb, realistic parameters. related pairs dimension magnetic field shown discussed. universal as they only rely on large-distance properties. Graphic abstract