Do it!

You should search on Ambien because it's been discussed here before, but my husband and I- neither of us into pill-taking in general- always take it on transatlantic flights. Yes, 4 hours of sleep is nice, especially if it's in place of zero (which happened to us a lot). I've never felt "hung over" on arrival. One piece of advice I've read is to take it only after you're sure the plane has on its way- you don't want to take it, zone out and then have to go back to the terminal.

I also took one a couple of days into a business trip in Munich when I woke up at 1 AM and couldn't get back to sleep. Now, if we're going to Europe, we don't leave home without it.