# Classical many-body time crystals

## TL;DR

This paper introduces a simple classical framework for realizing many-body time crystals using coupled resonators, clarifies the distinction between single-mode and many-body symmetry breaking, and demonstrates the concept experimentally with mechanical oscillators.

## Contribution

It provides a pedagogical classical approach to many-body time crystals and experimentally demonstrates their realization with coupled mechanical oscillators.

## Key findings

- Classical period-doubling bifurcation theory explains time crystal formation.
- Experimental demonstration with coupled mechanical oscillators.
- Clear distinction between single-mode and many-body time-translation symmetry breaking.

## Abstract

Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a many-body state, alongside several experimental realizations. In this work, we provide a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators. In our analysis, we use classical period-doubling bifurcation theory and present a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition. We experimentally demonstrate this paradigm using coupled mechanical oscillators, thus providing a clear route for time crystals realizations in real materials.