Arbitrary synthetic dimensions via multiboson dynamics on a one-dimensional lattice

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