Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror

TL;DR

This paper analyzes the classical dynamics of particles bouncing on an oscillating mirror, establishing a foundation for quantum time crystal phenomena in ultra-cold atoms by deriving an effective Hamiltonian and demonstrating engineered resonant behaviors.

Contribution

It introduces a classical model for particles on an oscillating mirror, deriving an effective Hamiltonian that enables engineering of particle dynamics for quantum time crystal research.

Findings

Particles can be resonantly driven to mimic higher-dimensional crystalline structures

Effective secular Hamiltonian describes resonant motion of particles

System can be used as a basis for quantum time crystal experiments

Abstract

We consider classical dynamics of a 1D system of $N$ particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for resonant motion of the particles. Proper choice of time periodic oscillations of the mirror allows for engineering of the effective behaviour of the particles. In particular, the system can behave like a $N$-dimensional fictitious particle moving in an $N$-dimensional crystalline structure. Our classical analysis constitutes a basis for quantum research of novel time crystal phenomena in ultra-cold atoms bouncing on an oscillating atom mirror.