# Multiple-period Floquet states and time-translation symmetry breaking in quantum oscillators

## TL;DR

This paper investigates how small quantum oscillators can exhibit broken time-translation symmetry through period tripling, demonstrating robustness over long timescales and under weak decoherence.

## Contribution

It introduces the concept of multiple-period Floquet states in small quantum systems and analyzes their stability and robustness against decoherence.

## Key findings

- Period tripling persists for exponentially long times under moderate driving.
- Weak decoherence further stabilizes the period tripling.
- The study bridges behavior between large and small quantum systems.

## Abstract

We study the breaking of the discrete time-translation symmetry in small periodically driven quantum systems. Such systems are intermediate between large closed systems and small dissipative systems, which both display the symmetry breaking, but have qualitatively different dynamics. As a nontrivial example we consider period tripling in a quantum nonlinear oscillator. We show that, for moderately strong driving, the period tripling is robust on an exponentially long time scale, which is further extended by an even weak decoherence.