Metamaterial model of a time crystal

TL;DR

This paper proposes a metamaterial-based model of a time crystal using hyperbolic metamaterials, demonstrating an analogy with Minkowski spacetime that challenges previous notions of time crystal non-existence.

Contribution

It introduces a novel metamaterial model of a time crystal based on hyperbolic metamaterials and spacetime analogy, providing new insights into time crystal properties.

Findings

The model mimics time crystal behavior using light propagation in metamaterials.

The energy spectrum lacks a static ground state, challenging previous proofs.

The approach offers a new platform for studying time crystals in engineered materials.

Abstract

Propagation of monochromatic extraordinary light in a hyperbolic metamaterial is identical to propagation of massive particles in a three dimensional effective Minkowski spacetime, in which the role of a timelike variable is played by one of the spatial coordinates. We demonstrate that this analogy may be used to build a metamaterial model of a time crystal, which has been recently suggested by Wilczek and Shapere. It is interesting to note that the effective single-particle energy spectrum in such a model does not contain a static ground state, thus providing a loophole in the proof of time crystal non-existence by P. Bruno.