Napping is actually a big part of the culture. You'll see many people catching naps on trains, buses, and other public places, even while standing up.
Japan has its own word "inemuri" for the practice of sleeping on the job, which is sometimes even faked to make it look like they're working hard.
http://en.wikipedia.org/wiki/Inemuri
Huh. Definitely not a part of American work culture - it's likely you'll wake up with a pink slip taped to your face.