Let's say you do everything well to have a good sleep: no excitation before, light diner, good position in bed, ... Also given you sleep as much as you need too and wake up naturally, is it better to sleep from 9pm to, say, 4am or from midnight to 6am? These hours are examples, so there may be better ones, depending of the answer.
If you have an Android phone, find out yourself. Sleep as Android is a really good application for tracking sleep, though you'd have to pay a little extra for the visual statistics.
Interestingly, the statistics show that I sleep deepest when I fall asleep at 5 AM. But this is most likely due to being exhausted wasting the night on something. I get a lot of deep sleep near 11 PM as well, compared to the hours in between.
But sleep quality itself actually differs widely.
I don't think any research on this is actually very reliable, because there's too many factors that can't be controlled, so I'd advise that you just try it out for yourself.