Space-time crystals of trapped ions

TL;DR

This paper proposes a method to create space-time crystals using trapped ions in a ring-shaped potential, demonstrating persistent rotation and temporal order, which opens new avenues for exploring many-body physics.

Contribution

It introduces a novel experimental setup for realizing space-time crystals with trapped ions and analyzes their robustness and temperature effects.

Findings

Ions form a stable spatial ring crystal due to Coulomb repulsion.

Persistent rotation of the ion crystal leads to temporal order, creating a space-time crystal.

Space-time crystals are robust and observable under experimental conditions.

Abstract

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.