Inseparable time-crystal geometries on the M\"obius strip

TL;DR

This paper demonstrates how to realize inseparable 2D time lattices with M"obius strip geometry using ultra-cold atoms bouncing between oscillating mirrors, enabling exploration of novel condensed matter phenomena in time.

Contribution

It introduces a method to create M"obius strip-shaped time lattices with ultra-cold atoms and shows how to control interactions and hopping in these systems.

Findings

Realization of M"obius strip time lattices with ultra-cold atoms.

Control of long-range interactions and hopping between atoms.

Implementation of a Lieb lattice model with flat bands.

Abstract

Description of periodically and resonantly driven quantum systems can lead to solid state models where condensed matter phenomena can be investigated in time lattices formed by periodically evolving Wannier-like states. Here, we show that inseparable two-dimensional time lattices with the M\"obius strip geometry can be realized for ultra-cold atoms bouncing between two periodically oscillating mirrors. Effective interactions between atoms loaded to a lattice can be long-ranged and can be controlled experimentally. As a specific example we show how to realize a Lieb lattice model with a flat band and how to control long-range hopping of pairs of atoms in the model.