If ants go to sleep, they certainly don't at a time that we know of. I mean, you could wake up in the dead of the night, go to your kitchen, and come across at least one ant rushing to get bread or leftover cake crumbs. So, we know that their hour clock isn't the same as ours.The thing is, ants only take power naps and those too short ones, and they don't have a set bedtime either and I suppose that answers the question, they do sleep, just not when you do. 

The thing is, ants do go to sleep. I mean, how else would they function the way that they do? The only difference is that they don't go to sleep at a time that we do, they have a completely different schedule and dare I say, a far more productive one.  As a matter of fact, an interesting point to know is that an ant takes about 250 naps per day and considering how a day only has 24 hours at most, you can imagine how short the naps would be. The entire time that they sleep only adds up to 4 hours at most! 

Ants take power naps for extremely short intervals during the day. This probably explains why you'll find an ant at any given time of the day.