The Atreides Empire was the term by which the Imperium was known when it was ruled by House Atreides. It was established when the Duke Paul Atreides successfully led a Fremen uprising on Arrakis against the Corrino Empire. One of the other Great Houses, House Harkonnen, was also destroyed in this uprising.
The commencement of the Atreides Empire was marked by the moving of the imperial seat from Kaitain to Arrakis.
Paul, as Muad'Dib ruled the empire for twelve years, before he transferred control to his sister, Alia Atreides as Regent. Some years after this, Paul's son Leto Atreides II ascended to the throne.
Thanks to his transformation into a human-sandworm hybrid, Leto II, ruled the empire for some 3,500 years. Upon his death the "Atreides Empire", and indeed all forms of empire in the known universe, officially ended. Atreides descendants flourished, however.