Stabilization of three-body resonances to bound states in a continuum

We present a theoretical study of resonance lifetimes in a two-component three-body system, focusing on the decay of three-body resonances into a deep dimer and an unbound particle. Previously, we demonstrated that the resonance widths exhibit a damped oscillatory behavior as a function of the mass ratio, with widths vanishing entirely at certain values. A resonance with vanishing width can be interpreted as a stable bound state in the continuum, a phenomenon not yet observed in cold-atom systems. In this talk we present an effective two-channel model which shows that this stabilization arises from a fundamental overlap integral that can be tuned to zero by adjusting the mass ratio. Moreover, this analysis reveals that also other parameters, e.g. an external magnetic field, can induce the same effect. We illustrate this mechanism with two examples: a mass-imbalanced system in 1D, where an approximate analytical expression is derived, and a system of three identical bosons in 3D, closely related to the Efimov scenario.