Achieving translational symmetry in trapped cold ion rings

TL;DR

This paper demonstrates the preservation of translational symmetry in a small ring of trapped cold ions, enabling detailed quantum many-body physics studies with single-particle control.

Contribution

It achieves and verifies translational symmetry in a small ion ring, a significant step for quantum simulation and studying symmetry-related phenomena at the single-particle level.

Findings

Translational symmetry is preserved at millikelvin temperatures.

Up to fifteen 40Ca+ ions are crystallized in a ring with periodic boundary conditions.

Symmetry breaking effects are minimized to enable quantum control.

Abstract

Spontaneous symmetry breaking is a universal concept throughout science. For instance, the Landau-Ginzburg paradigm of translational symmetry breaking underlies the classification of nearly all quantum phases of matter and explains the emergence of crystals, insulators, and superconductors. Usually, the consequences of translational invariance are studied in large systems to suppress edge effects which cause undesired symmetry breaking. While this approach works for investigating global properties, studies of local observables and their correlations require access and control of the individual constituents. Periodic boundary conditions, on the other hand, could allow for translational symmetry in small systems where single particle control is achievable. Here, we crystallize up to fifteen 40Ca+ ions in a microscopic ring with inherent periodic boundary conditions. We show the ring's translational symmetry is preserved at millikelvin temperatures by delocalizing the Doppler laser cooled ions. This establishes an upper bound for undesired symmetry breaking at a level where quantum control becomes feasible. These findings pave the way towards studying quantum many-body physics with translational symmetry at the single particle level in a variety of disciplines from simulation of Hawking radiation to exploration of quantum phase transitions.