Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice

TL;DR

This paper introduces a theoretical framework that maps N-boson systems on one-dimensional lattices to higher-dimensional synthetic lattices, enabling analysis of exotic states and multi-boson dynamics with potential quantum engineering applications.

Contribution

It presents a novel method to construct arbitrary synthetic dimensions using multi-boson dynamics, expanding the understanding of complex eigenstates and wavepacket motion in synthetic lattices.

Findings

Demonstration of edge states in two-boson SSH synthetic lattices

Identification of interface states with interactions

Prediction of weakly-bound triplon states in three-boson lattices

Abstract

The synthetic dimension, a research topic of both fundamental significance and practical applications, is attracting increasing attention in recent years. In this paper, we propose a theoretical framework to construct arbitrary synthetic dimensions, or N-boson synthetic lattices, using multiple bosons on one-dimensional lattices. We show that a one-dimensional lattice hosting N indistinguishable bosons can be mapped to a single boson on a N-dimensional lattice with high symmetry. Band structure analyses on this N-dimensional lattice can then be mathematically performed to predict the existence of exotic eigenstates and the motion of N-boson wavepackets. As illustrative examples, we demonstrate the edge states in two-boson Su-Schrieffer-Heeger synthetic lattices without interactions, interface states in two-boson Su-Schrieffer-Heeger synthetic lattices with interactions, and weakly-bound triplon states in three-boson tight-binding synthetic lattices with interactions. The interface states and weakly-bound triplon states have not been thoroughly understood in previous literatures. Our proposed theoretical framework hence provides a novel perspective to explore the multi-boson dynamics on lattices with boson-boson interactions, and opens up a future avenue in the fields of multi-boson manipulation in quantum engineering.