Engineering long-range interacting spin systems with ultracold atoms offers the possibility to explore exotic magnetically ordered phases in strongly-correlated scenarios. Quantum gases in optical cavities provide a versatile experimental platform to further engineer photon-mediated interactions and access the underlying microscopic processes by probing the cavity field. Here, we study a two-component spin Bose-Hubbard system with cavity-mediated interactions. We provide a comprehensive overview of its phase diagram and transitions in experimentally relevant regimes. The interplay of different energy scales yields a rich phase diagram with superfluid and insulating phases exhibiting density modulation or spin ordering. In particular, the combined effect of contact and global-range interactions gives rise to an antiferromagnetically ordered phase for arbitrarily small spin-dependent light-matter coupling, while global-range and inter-spin contact interactions introduce regions of instability and phase separation in the phase diagram. We further study the low energy excitations above the antiferromagnetic phase. Besides particle-hole branches, it hosts spin-exchange excitations with a tunable energy gap. The studied lattice model can be readily realized in cold-atom experiments with optical cavities.

• Received 20 October 2022
• Revised 3 March 2023
• Accepted 14 April 2023

DOI:https://doi.org/10.1103/PhysRevResearch.5.L032003

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society