Atomic Data is not necessarily bound to a single serialization format. It's fundamentally a data model, and that's an important distinction to make.
However, it's recommended to use
JSON-AD (more about that on the next page), which is specifically designed to be a simple, complete and performant format for Atomic Data.
Atomic Data is designed to be serializable to clean, simple JSON, for usage in (client) apps that don't need to know the full URLs of properties.
Since Atomic Data is a strict subset of RDF, RDF serialization formats can be used to communicate and store Atomic Data, such as N-Triples, Turtle, HexTuples, JSON-LD and other RDF serialization formats. However, not all valid RDF is valid Atomic Data. Atomic Data is more strict. Read more about serializing Atomic Data to RDF in the RDF interoperability section.
Some experimental ideas for Atomic Data serialization are written here.