Breathing Modes and Hidden Symmetry of Trapped Atoms in 2D

TL;DR

This paper explores the universal breathing modes of atoms in 2D harmonic traps, linking them to a hidden SO(2,1) symmetry that enables pulsating solutions and can be used to probe experimental systems.

Contribution

It reveals the connection between breathing modes and a hidden SO(2,1) symmetry in 2D trapped atoms, providing a new perspective for analyzing their dynamics.

Findings

Breathing modes are connected to a hidden SO(2,1) symmetry.

Pulsating solutions can be constructed for quantum and nonlinear systems.

The symmetry offers a new method to probe 2D trapped atom experiments.

Abstract

Atoms confined in a harmonic potential show universal oscillations in 2D. We point out the connection of these ''breathing'' modes to the presence of a hidden symmetry. The underlying symmetry SO(2,1), i.e. the two dimensional Lorentz group, allows pulsating solutions to be constructed for the interacting quantum system and for the corresponding nonlinear Gross-Pitaevskii equation. We point out how this symmetry can be used as a probe for recently proposed experiments of trapped atoms in 2D.