Melatonin. Ambien (zolpidem) has been studied and found to have some benefit for jet lag, however I generally recommend melatonin taken 30 minutes before the intended bedtime; it is better tolerated and a more natural way to adjust to a new time zone.
See below. Yes, Ambien (zolpidem) is prescribed to regularize the sleep cycle and it is safe as the fda has tested it for short-term use for inability to fall asleep. However, the elderly and those with other medical problems or sedating medications are at greater risk of side effects, including daytime sleepiness.