From Life Hack:
“So what does this all mean? It means that your goal during a nap is to enter the REM sleep phase quickly (this is where most dreaming occurs), and to wake up as soon as the REM sleep phase is over. If you sleep past the REM phase you’ll enter deeper phases of sleep and it will be really difficult to get up!
The only reason this is difficult is that everyone sleeps differently. For most people, their optimal nap time (where they can wake up just as they finish REM) is between 15 and 30 minutes, but you’ll have to test to find yours precisely.
What makes it more difficult is that you have to take into account how long it takes you to fall asleep. When you are first perfecting your naps, it could take quite a while to fall asleep, so I’d suggest starting with a 30–35 minute nap, and working your way down.
Don’t be surprised if after a 30 minute nap you are exhausted. You may have gone right through REM into a deeper sleep phase. It will feel like being woken up in the middle of the night, and during these times I’ve had trouble with even the most basic tasks like keeping my balance or forming sentences.
Each day, try a different length of nap, reducing the time by 3–5 minutes, and record your energy levels. As you learn to fall asleep quicker, and close in on your optimal time, you’ll notice a remarkable thing: it’s possible to wake up from a nap totally refreshed and alert”