Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice

TL;DR

This paper investigates how to create uniform synthetic magnetic fields in optical lattices by shaking the lattice, comparing different protocols to identify methods that produce uniform flux and effective mass, with implications for cold-atom and photonic systems.

Contribution

The study provides a theoretical analysis of lattice-shaking protocols to generate uniform synthetic magnetic fields, introducing novel schemes that improve flux uniformity and effective mass control.

Findings

Identified shaking schemes that produce uniform magnetic flux

Compared moving lattice methods with site-shaking protocols

Provided insights for cold-atom and photonic experimental implementations

Abstract

Shaking a lattice system, by modulating the location of its sites periodically in time, is a powerful method to create effective magnetic fields in engineered quantum systems, such as cold gases trapped in optical lattices. However, such schemes are typically associated with space-dependent effective masses (tunneling amplitudes) and non-uniform flux patterns. In this work we investigate this phenomenon theoretically, by computing the effective Hamiltonians and quasienergy spectra associated with several kinds of lattice-shaking protocols. A detailed comparison with a method based on moving lattices, which are added on top of a main static optical lattice, is provided. This study allows the identification of novel shaking schemes, which simultaneously provide uniform effective mass and magnetic flux, with direct implications for cold-atom experiments and photonics.