Weakly bound molecules trapped with discrete scaling symmetries

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.

9 pages, 7 figures; (v2) minor improvements; (v3) expanded and published

References in corpus (5)

• Weakly bound dimers of fermionic atoms
• Universal Relations for Identical Bosons from 3-Body Physics
• Analytical solution of the bosonic three-body problem
• Single-Particle Momentum Distribution of an Efimov trimer
• Liberating Efimov physics from three dimensions

Cited by in corpus (8)

• Two-field optical methods to control magnetic Feshbach resonances
• Designer Spatial Control of Interactions in Ultracold Gases
• Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions
• Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance
• Generalized Efimov effect in one dimension
• Hydrodynamics with spacetime-dependent scattering length
• Time fractals and discrete scale invariance with trapped ions
• Efimov effect for two particles on a semi-infinite line