First of all, you cannot reach REM sleep in a matter of minutes; during the night, it takes about 2–3 hours of sleep before you reach the REM state. It’s highly unlikely you will get REM sleep during a daytime nap.
Second, you do not need to reach REM sleep in order to have a restful nap. The numbers are different for everyone, but the generally accepted number is 20 minutes. You might not feel like you’re sleeping, but you will be reenergized from sitting still with your eyes closed for 20 minutes. Be careful not to do it for too long, as you will feel worse.
I used to do this after work but before night classes and if I didn’t get my 20 minutes at the university library, I couldn’t focus during class. I didn’t know that what I was doing was “power-napping” but it certainly felt nice to know that science backed up what I had worked out for myself.