I've noticed the same kind of distraction-free productivity in the wee hours and thought about starting my day at midnight, but usually I have a hard time taking my hands off whatever task is on hand. Consequently, I am usually a night owl who wakes up nearly at noon (I'm a student, as well), and when I actually need to be somewhere in the morning, I power through with a few bags of black tea.

I admit the 5pm bedtime schedule is a lot healthier and syncs with the 9-to-5 work schedule nicely, though.