Quantum scar affecting the motion of three interacting particles in a circular trap

TL;DR

This paper predicts and analyzes a quantum scar phenomenon in a three-particle system in a circular trap, linking quantum eigenstates to classically unstable trajectories, with potential experimental realization.

Contribution

It introduces a new type of quantum scar in a few-body system, explaining its origin via classical chaos and unstable trajectories, supported by numerical calculations.

Findings

Identification of scarred eigenstates linked to classical unstable trajectories

Full explanation of scar towers based on classical chaos

Proposal for experimental observation using Rydberg atom traps

Abstract

We theoretically propose a quantum scar affecting the motion of three interacting particles in a circular trap. We numerically calculate the quantum eigenstates of the system and show that some of them are scarred by a classically unstable periodic trajectory, in the vicinity of which the classical analog exhibits chaos. The few-body scar we consider is stabilized by quantum mechanics, and we analyze it along the lines of the original quantum scarring mechanism [Heller, Phys. Rev. Lett. 53, 1515 (1984)]. In particular, we identify towers of scarred quantum states which we fully explain in terms of the unstable classical trajectory underlying the scar. Our proposal is within experimental reach owing to very recent advances in Rydberg atom trapping.