Abstract
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 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 an 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 wave packets. 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 research. Our proposed theoretical framework hence provides an interesting perspective to explore the multiboson dynamics on lattices with boson-boson interactions, and opens up a future avenue in the field of multiboson manipulation in quantum engineering.
Highlights
Dimensionality is one of the most important concepts in modern physics
We propose a theoretical framework to treat the multiboson dynamics in a one-dimensional lattice as an N-boson synthetic lattice by applying exchange symmetry restrictions to the wave function
For complicated Hamiltonians with boson-boson interactions, projected band structures could be understood from the full N-dimensional band structure, and nontrivial multiboson states
Summary
Dimensionality is one of the most important concepts in modern physics. In condensed-matter physics, systems with different dimensionalities exhibit vastly different behaviors. Repulsively bound boson pairs, called doublons, have been unveiled as a result of the Bose-Hubbard Hamiltonian [31] Following this important discovery, quantum problems of two-particle states with one-dimensional (1D) interactive Hamiltonians, such as the tight-binding Bose-Hubbard model [32]; the tight-binding Bose-Hubbard model with a parabolic potential [33], with a small impurity potential [34], and with nonlocal interactions [35,36,37]; and the SuSchrieffer-Heeger (SSH) Bose-Hubbard model with nonlocal interactions [38,39,40,41,42]; as well as two-particle problems with Bloch oscillation in an external electrical field [43,44,45], have been investigated with very broad interest in both condensedmatter and optical societies.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
