Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice
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.
Cite
@article{arxiv.2104.10389,
title = {Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice},
author = {Dali Cheng and Bo Peng and Da-Wei Wang and Xianfeng Chen and Luqi Yuan and Shanhui Fan},
journal= {arXiv preprint arXiv:2104.10389},
year = {2021}
}