Quantum Lissajous Scars

Abstract

A quantum scar - an enhancement of a quantum probability density in the vicinity of a classical periodic orbit - is a fundamental phenomenon connecting quantum and classical mechanics. Here we demonstrate that some of the eigenstates of the perturbed two-dimensional anisotropic (elliptic) harmonic oscillator are strongly scarred by the Lissajous orbits of the unperturbed classical counterpart. In particular, we show that the occurrence and geometry of these quantum Lissajous scars are connected to the anisotropy of the harmonic confinement, but unlike the classical Lissajous orbits the scars survive under a small perturbation of the potential. This Lissajous scarring is caused by the combined effect of the quantum (near) degeneracies in the unperturbed system and the localized character of the perturbation. Furthermore, we discuss experimental schemes to observe this perturbation-induced scarring.

6 pages, 3 figures

References in corpus (6)

• Probing many-body dynamics on a 51-atom quantum simulator
• Chaos-driven dynamics in spin-orbit coupled atomic gases
• Controllable quantum scars in semiconductor quantum dots
• Spin-droplets in confined quantum Hall systems
• Half-Integer Filling Factor States in Quantum Dots
• Polyatomic trilobite Rydberg molecules in a dense random gas