Clarify the classical–quantum chaos connection in trapped ion–atom systems

Determine the physical mechanism that reconciles classical non-hyperbolic chaotic scattering in Paul-trapped ion–atom collisions—as evidenced by power-law complex lifetimes and fractal scattering observables—with the reported absence of quantum-chaos spectral signatures in a one-dimensional quantum mechanical treatment of collisions between a trapped Yb+ ion and a Li atom; elucidate the correspondence between classical chaos and quantum chaos in trapped ion–atom systems.

Background

The paper presents extensive classical simulations of atom–ion collisions in a Paul trap, demonstrating non-hyperbolic chaotic scattering characterized by fractal structures in observables and power-law complex lifetimes. These results link ion heating induced by the time-dependent trap with the onset of chaos and show that heavier, colder atoms more readily form long-lived complexes.

However, a full one-dimensional quantum mechanical treatment of Yb+–Li collisions reported elsewhere did not exhibit the expected spectral signatures of quantum chaos. The authors explicitly note that the reason for this apparent contradiction is not clear and call for further research to elucidate how classical chaotic dynamics correspond to (or fail to manifest as) quantum-chaos signatures in trapped ion–atom systems.