Efimov physics in the complex plane

TL;DR

This paper explores how two-body loss, modeled by a complex scattering length, affects Efimov states, revealing new bound states with extended lifetimes and a generalized geometric scaling law in the complex energy plane.

Contribution

It introduces a generalized framework for Efimov physics with complex scattering lengths, predicting novel bound states with unique lifetime properties.

Findings

Discovery of Efimov states with positive real energies and extended lifetimes.

Validation of a generalized geometric scaling law in the complex energy plane.

Identification of conditions where three-body states surpass two-body state lifetimes.

Abstract

Efimov effect is characterized by an infinite number of three-body bound states following a universal geometric scaling law at two-body resonances. In this paper, we investigate the influence of two-body loss which can be described by a complex scattering length $a_c$ on these states. Interestingly, because of the complexity of the scattering length $a_c$, the trimer energy is no longer constrained on the negative real axis, and it is allowed to have a nonvanishing imaginary part and a real part which may exceed the three-body or the atom-dimer scattering threshold. Indeed, by taking the $^{133}$Cs-$^{133}$Cs-$^6$Li system as a concrete example, we calculate the trimer energies by solving the generalized Skorniakov-Ter-Martirosian equation and find such three-body bound states with energies that have positive real parts and obey a generalized geometric scaling law. Remarkably, we also find that in some regions these three-body bound states have longer lifetimes compared with the corresponding two-body bound states. The lifetimes for these trimer states can even tend to infinity. Our work paves the way for the future exploration of few-body bound states in the complex plane.