From nanoelectronics to string theory, the dimensionality of space provides a fundamental constraint in modern physics research. This constraint, however, can be overcome with the introduction of the synthetic dimensions. The concept of synthetic dimensions adds to the dimensionality of physical systems in real space. Physical phenomena unique to high-dimensional systems can thus be equivalently simulated and explored in low-dimensional experimental platforms which features easier manipulation. Conventionally, methods of constructing synthetic dimensions include connecting the internal degrees of freedom of particles, for example, the frequencies, orbital angular momenta, and arrival times of photons.

In this paper, beyond these available methods to synthesize extra dimensions, we propose a theoretical framework that constructs arbitrary synthetic dimensions using multiple bosons in a one-dimensional space. Within this theoretical framework, a one-dimensional lattice hosting N indistinguishable bosons is mathematically converted to an N-dimensional synthetic lattice. As a result, the band structure analysis of a single boson in a high dimensional system can be used to predict the behavior of a multi-boson state in one dimension. 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. These results provide a novel perspective to the studies of both synthetic dimensions and many-body quantum physics. We expect that these findings may find potential applications in the fields of quantum computations, quantum simulations and quantum information processing.

Fig. 1. (a) A 1D tight-binding lattice hosting two bosons. (b) The corresponding two-boson synthetic lattice. (c) 2D band structure of the lattice in (b).

Fig. 2. (a) The edge state in two-boson Su–Schrieffer–Heeger synthetic lattices without interactions. (b) The interface state in two-boson Su–Schrieffer–Heeger synthetic lattices with interactions. (c) The weakly bound triplon state in three-boson tight-binding synthetic lattices with interactions.

This research was published in “Dali Cheng, Bo Peng, Da-Wei Wang, Xianfeng Chen, Luqi Yuan, and Shanhui Fan. Arbitrary synthetic dimensions via multiboson dynamics on a one-dimensional lattice. Physical Review Research 3, 033069 (2021)”.

Link: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.033069