Which is the correct way of asking the question "Are you logged in"? Or "Have you logged in"?
Both are correct - it ultimately depends on the question that you wish to ask.
If you were to ask:
Are you logged in?
Then you are asking whether the user is currently logged into a particular system at the present moment.
Whereas, if you were to ask:
Have you logged in?
Then you are asking whether, at some point in time, the user has performed the action of logging into a particular system.