We investigate the formation of three-body bound states in the continuum by tracing pole trajectories in the complex energy plane under variation of system parameters. Using a one-dimensional model of two identical bosons and a distinguishable particle interacting via Gaussian potentials, we systematically vary the interaction strength, interaction range, and mass ratio. Our results confirm the parametric nature of few-body bound states in a continuum (BIC) and extend this characterization to a broader set of system parameters. Specifically, we find that variations of both interaction parameters and the mass ratio can lead to the formation of at least one three-body BIC. However, the exact shape of trajectories differs, and for the mass ratio variation we find a more regular pattern with multiple BIC locations. These results suggest that the mechanism of few-body BIC formation is more sensitive to the kinematic structure of the problem than to the specific details of the two-body interaction.
Few-body bound states have been extensively explored in cold atomic gases with a desire to realize large molecular complexes. Here, we investigate the formation of trimers in an infinite one-dimensional lattice with hard-core two- and three-body interactions of relevance to Rydberg atoms and polar molecules in optical lattices, and other physical systems such as the fractional Hall states. We determine the stability regions for attractively and repulsively bound trimers. We discover a regime of large spatially extended trimers that are stabilized by the interplay of attractive two-body,
U , and repulsive three-body,
V , interactions and persist despite extremely large
V. These bound states present a new direction in the search for large few-body complexes in cold atoms.
Three-body resonances are ubiquitous in quantum few-body physics and are characterized by a finite lifetime before decaying into continuum states of their composing subsystems. In this work we present a theoretical study on the possibility to stabilize three-body resonances to so-called bound states in a continuum: resonances with vanishing width that do not decay. Within a two-channel approach we unveil the underlying mechanism and show how the lifetime can be made infinitely long by a continuous tuning of system parameters. The validity of our theory is illustrated in two different examples: a mass-imbalanced system in one dimension and a system of three identical bosons in three dimensions, relevant to Efimov physics. Crucially, for the latter we find that one of the parameters that can be tuned to achieve a three-body bound state in a continuum is an external magnetic field, a common tunable variable in cold-atom experiments. Due to the generality of this stabilization effect, it is expected to be applicable to a wide range of unstable few-body systems, opening new perspectives for fundamental studies as well as technical applications.