This last trip was an exception. It took several days before I got on European time. I suspect this was due to the Ambien I was taking and other factors that kept me from my usual ordeal (arriving in Europe) of arriving in the morning quite trashed, taking a several-hour afternoon nap followed by a very painful alarm-driven wakeup, shower, dinner, then a crash for the night. Come morning, I'm at least 90% functional.
I tried Ambien, once. I either barfed it up immediately, or managed to hold it until my eyes opened.
I found the best thing on long trips (Pak, for example) was to take naps all the way over, and throw out the clock. I napped from O’Hare to Heathrow, maybe a total of five hours, napped between flights (maybe five hours all told) and napped again from Heathrow to Islamabad.
Jet lag was not much of an issue, so when I plan to travel out of my time zone, I take some benedryl with me, and that helps me nap.
I took naps on the way home, as well, so the entire thing was not really as traumatic as it was the first time I crossed the Atlantic.