# Engineered Nearest-Neighbour Interactions with Doubly Modulated Optical Lattices

## TL;DR

This paper proposes a method to engineer specific quantum interactions in optical lattices using doubly modulated fields, enabling control over quantum phases like Mott insulators and density waves.

## Contribution

It introduces a novel doubly modulated Bose-Hubbard model that allows tuning of nearest-neighbour interactions and density-assisted tunnelling in optical lattices.

## Key findings

- Doubly modulated fields induce nearest neighbour interactions.
- Designing bi-chromatic driving patterns enables phase control.
- Realization of Mott insulator and density wave phases.

## Abstract

Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and predict the emergence of the nearest neighbour interaction and density-assisted tunnelling. By specifically designing a bi-chromatic driving pattern for a one dimensional lattice, we demonstrate that the doubly modulated fields can be tuned to realize desired quantum phases, e.g. the Mott insulator phase with selective defects, and density wave phase.