Synthetic space in photonics is of great interest and attracts many attentions recently. With the parameter space, one is possible to explore high-dimensional physics in a synthetic space including both the synthetic momentum dimension and the spatial dimension.

We explore one-dimensional atomic arrays in a spatially-periodic magnetic field. Photon-mediated dipole-dipole interactions and Zeeman shift induced by the magnetic field are considered. By involving the synthetic momentum dimension from the parameter in the magnetic field, we realize an effective two-dimensional Hofstadter-butterfly-like spectrum. Moreover, we find that the system exhibits tunable super- and sub-radiant topological boundary states despite featuring long-range interaction. Our work shows effective manipulations of quantum states, which gives a key step towards applications in quantum information, quantum metrology, and quantum nonlinear optics.

LEFT: One-dimensional atomic array with the external magnetic field; RIGHT: The effective Hofstadter-butterfly-like spectrum

The paper has been published in Communications Physics with the title “Tunable super- and subradiant boundary states in one-dimensional atomic arrays”.

Link: https://doi.org/10.1038/s42005-019-0263-0