# Non-thermalization in trapped atomic ion spin chains

## TL;DR

This paper reviews how trapped ion systems are used to study non-ergodic phenomena like many-body localization, prethermalization, and discrete time crystals, revealing long-lived memory effects in quantum spin models.

## Contribution

It highlights recent experimental advances in observing non-ergodic phenomena in long-range interacting spin models using trapped ions.

## Key findings

- Observation of long-lived memory in static magnetizations
- Detection of persistent oscillations in a driven discrete time crystal
- Evidence of non-ergodic behavior in long-range quantum spin systems

## Abstract

Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatiotemporal resolution, decoupling from the external environment, and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin-models which are heralded by memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.