Weakly bound molecules trapped with discrete scaling symmetries

TL;DR

This paper introduces a tunable ultracold atom system where particles are trapped by a scattering length proportional to their distance from the center, exhibiting discrete scale invariance similar to Efimov states, and explores its implications for universal quantum physics.

Contribution

It presents a novel ultracold atom setup demonstrating discrete scaling symmetry and analyzes its violation in many-body systems, advancing understanding of Efimov physics and scale invariance.

Findings

Particles are trapped with a scattering length proportional to distance from the center.

Spectrum exhibits discrete scale invariance controlled by the scattering length slope.

Discrete scaling symmetry is violated for more than two bosons.

Abstract

When the scattering length is proportional to the distance from the center of the system, two particles are shown to be trapped about the center. Furthermore, their spectrum exhibits discrete scale invariance, whose scale factor is controlled by the slope of the scattering length. While this resembles the Efimov effect, our system has a number of advantages when realized with ultracold atoms. We also elucidate how the emergent discrete scaling symmetry is violated for more than two bosons, which may shed new light on Efimov physics. Our system thus serves as a tunable model system to investigate universal physics involving scale invariance, quantum anomaly, and renormalization group limit cycle, which are important in a broad range of quantum physics.