A topological vacuum is a family of degenerate ground states of the Young-Mills field, with zero field strength, but a non-trivial topological structure. They play a fundamental role in particle physics and quantum field theory, but have yet to be observed experimentally. Here we report the first theoretical proposal and experimental realization of a synthetic topological vacuum using atomic Bose-Einstein condensate clouds. Our setup provides a promising platform for demonstrating the basic concept that the vacuum, not the sky, has a rich spatial structure. Synthesize the vacuum Hamiltonian with phase number n = 1 and measure the associated Hopf index. Vacuums with topological number n = 2 are also realized, and we find that vacuums with different topological numbers have characteristic spin textures and hop links. Our work opens up opportunities to explore long-sought instantons associated with topological vacuums in tabletop experiments.
