Which is, apparently, when sperm whales sleep: While diving.
Scientists at St. Andrew's University tagged the well-known square-headed mammals -- the largest living animal with teeth, which I believe means the answer to "How did they tag them" is "Verrrrry carefully" -- and then recorded their behavior. They found that the whales catch 10-15 minute naps during their dives, which can go as deep as 1.8 miles, and actually sleep less than two hours a day (Note from cats: "That's insane!").
The article writer suggests that sperm whales literally drift off to sleep during these dives, probably comparing the relatively slow speed of the sleeping dive to their top speed of about 25 miles an hour. But I don't know if "drift" is the right word for something that averages more than 50 feet in length and forty-five tons in weight as do adult males. I'd think no matter how slowly it was moving, if something's that big you have to call it a "power nap."
Here at Discovery.com is a video of a pod of whales caught during naptime.