This is what happens when you take sleeping pills for a month. The first time that you try to sleep unaided, you get rebound insomnia. Insomnia -- just the thing you have been trying to avoid! Although I have not taken any of the drugs named in the JAMA article, I think this is the best term to define poor sleep after stopping sleep meds.
I had a night or two of this lovely condition, then I guess my body relaxed back into natural sleep. Now I only wake up with hot flashes two or three times a night. That's natural sleep for me.