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

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.

14 pages, 3 figures

References in corpus (6)

• A Brief History of Time Crystals
• Condensed Matter Physics in Time Crystals
• Anderson localization and Mott insulator phase in the time domain
• Many-body localization caused by temporal disorder
• Many-Body Effects and Quantum Fluctuations for Discrete Time Crystals in Bose-Einstein Condensates
• Controlled preparation of phases in two-dimensional time crystals

Cited by in corpus (4)

• Synthetic dimensions for topological and quantum phases: Perspective
• Classical Phase Space Crystals in an Open Environment
• Time crystal embodies chimeralike state in periodically driven quantum spin system
• Formation of Complex Discrete Time Crystals with Ultracold Atoms