# Quantum state preparation for coupled period tripling oscillators

## TL;DR

This paper explores the quantum transition to correlated states in coupled oscillators exhibiting period tripling, highlighting the role of geometric phases and phase correlations in the quantum regime.

## Contribution

It introduces a quantum framework for understanding period tripling in coupled oscillators, emphasizing the role of geometric phases and phase correlations.

## Key findings

- Correlations form between oscillation phases during the transition.
- Transient symmetry breaking occurs due to geometric phases.
- Wigner distribution shows a minimum at zero amplitude in the quantum regime.

## Abstract

We investigate the quantum transition to a correlated state of coupled oscillators in the regime where they display period tripling in response to a drive at triple the eigenfrequency. Correlations are formed between the discrete oscillation phases of individual oscillators. The evolution toward the ordered state is accompanied by the transient breaking of the symmetry between seemingly equivalent configurations. We attribute this to the nontrivial geometric phase that characterizes period tripling. We also show that the Wigner distribution of a single damped quantum oscillator can display a minimum at the classically stable zero-amplitude state.