# Breaking rotational symmetry in a trapped-ion quantum tunneling rotor

## TL;DR

This paper explores how flipping the spin of an ion in a trapped-ion quantum tunneling rotor breaks its rotational symmetry, affecting its quantum tunneling dynamics and coupling between spin and rotation.

## Contribution

It introduces a theoretical framework describing the quantum dynamics of a trapped-ion QTR, especially under spin flips and magnetic fields, revealing symmetry-breaking effects.

## Key findings

- Spin flip breaks rotational symmetry of the QTR.
- Coupling between spin state and rotational motion is induced.
- Quantum tunneling dynamics are altered by symmetry breaking.

## Abstract

A trapped-ion quantum tunneling rotor (QTR) is in a quantum superposition of two different Wigner crystal orientations. In a QTR system, quantum tunneling drives the coherent transition between the two different Wigner crystal orientations. We theoretically study the quantum dynamics of a QTR, particularly when the spin state of one of the ions is flipped. We show that the quantum dynamics of an $\it{N}$-ion QTR can be described by continuous-time cyclic quantum walks. We also investigate the quantum dynamics of the QTR in a magnetic field. Flipping the spin state breaks the rotational symmetry of the QTR, making the quantum-tunneling-induced rotation distinguishable. This symmetry breaking creates coupling between the spin state of the ions and the rotational motion of the QTR, resulting in different quantum tunneling dynamics.