Exploring the Strongly-Interacting Regime of Effective Multi-Body Interactions in a Trapped Ultracold Atom System

A two-body interaction or force between quantum particles is ubiquitous in nature, and the microscopic description in terms of the bare two-body interaction is the basis for quantitatively describing interacting few- and many-body systems. Alternatively, the effective description in terms of an effective two-body interaction successfully captures the essence of the systems. However, for several important observations, the explanation in terms of an effective two-body interaction is not satisfactory, and the effective three-body interaction has played an essential role in understanding the systems. In this study, we investigate a few-body system comprising of ultracold bosons tightly confined in a deep optical lattice site, which is effectively described as zero-dimensional bosons. By combining an occupancy-resolving high-resolution laser spectroscopy with an inter-orbital Feshbach resonance controlling the bare two-body interaction over a wide range, we experimentally reveal the behaviors of few-atom systems in a strongly interacting regime. Our results, for which perturbative calculations do not provide proper explanations, serve as a valuable and precise benchmark for theoretical approaches to strongly interacting few-body systems. As one important illustration, we obtain a clear signature of an effective four-body interaction evidenced by the binding energies of four and more atoms. This work is an important step for our deeper understanding of strongly interacting few-body systems.