A Maxwell Fish-Eye Lens in a Bose-Einstein Condensate

TL;DR

This paper demonstrates an experimental realization of a Maxwell fish-eye lens analogue in a Bose-Einstein condensate by engineering the speed of sound for phonons, enabling perfect wave focusing and simulating spherical geometries.

Contribution

It introduces a method to create a gradient-index lens in a BEC for phonons, enabling wave focusing and geometric simulations not feasible in traditional optics.

Findings

Phonon wavefronts focus as predicted by theory.

Good agreement between experimental results and simulations.

Provides a new platform for wave propagation studies in ultracold atoms.

Abstract

We experimentally realize an analogue of the optical Maxwell fish-eye lens (MFEL) using phononic excitations in a Bose-Einstein condensate (BEC). A MFEL is characterized by a radially symmetric, spatially varying refractive index with the remarkable property that rays emitted from any point within the lens are perfectly focused at their image points. While the implementation of such gradient-index lenses is challenging in conventional optical systems, BECs offer a highly tunable platform in which the spatially varying speed of sound of collective excitations -- phonons, the acoustic-wave analogues of photons -- can be engineered and their dynamics observed in real time. Time-resolved measurements of phonon wavefronts reveal focusing behavior that shows good agreement with analytical theory and numerical simulations. This work provides both a geometric and physical framework for engineering effective refractive indices using ultracold atoms, and simulating wave propagation on effective spherical geometries.