When you start the game, you'll notice a branch of your research tree is locked. This is the Elysium tech. To unlock it, you must first find an Asimov Override. Easiest way is to purchase one from a trader, with upgrade traders and generalists being the best bet. Once you've installed an Asimov Override into your ship's computer, you can then research Elysium. As soon as the research is complete, all you need to do is click on your Stasis Array and activate Elysium. This is irreversible, so if you're only doing this for the achievement, make sure to save beforehand if you don't want to sacrifice your colonists for an achievement.