Airy wavepackets are Perelomov coherent states

TL;DR

This paper demonstrates that Airy wavepackets, known for their non-spreading and accelerating properties, are actually Perelomov coherent states, with their unique behavior rooted in Galilean invariance of the Schrödinger equation.

Contribution

It reveals the fundamental connection between Airy wavepackets and Perelomov coherent states, highlighting the role of Galilean invariance in their properties.

Findings

Airy wavepackets are Perelomov coherent states

Galilean invariance underpins their unique propagation

Optical experiments have realized these wavepackets

Abstract

Accelerating non-spreading wavepackets in nonrelativistic free particle system, with probability distribution having an Airy function profile, were discovered by Berry and Balazs (1979), and have been subsequently realised in several optical experiments. It is shown that these wavepackets are actually Perelomov coherent states. It is found that the Galilean invariance of the Schrodinger equation plays a key role in making these states unique and giving rise to their unusual propagation properties.