Synthetic Dimensions for Cold Atoms from Shaking a Harmonic Trap

TL;DR

This paper proposes a simple method to create synthetic dimensions in ultracold atoms using harmonic traps and periodic shaking, enabling simulation of magnetic fields and topological phenomena.

Contribution

It introduces a new, straightforward scheme to realize synthetic dimensions with harmonic traps and shaking, facilitating exploration of higher-dimensional topological physics in cold atom systems.

Findings

Realization of artificial magnetic fields in cold atoms

Observation of quantum Hall physics in synthetic dimensions

Reduction of energy under resonant driving

Abstract

We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time-modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realisation of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.