As far as I can tell the subjects in Inception need to sleep in order to dream and for going under fast and consistent sleep they use sedatives.
Now my question is how did Cobb manage to just fall asleep and dream in a matter of seconds, amidst that turmoil when Mal dies by the hand of Ariadne, to go save Saito?
If I recall correctly both Saito and Cobb are already in limbo at that point, so Cobb does not have to 'go down a level' merely go 'across'.
As we see him washed up on a shore before he meets Saito and there is a shore near the city he built we could assume that he has crossed the sea in some sort of imagined/constructed boat but has run into a storm or some sort of interference as he gets close to Saito.
I feel you want to know without using any sedatives in the dream, how could Cobb go to sleep so fast in the dream. I guess you need to understand several things.
Saito was already in the limbo state due to his death in upper dream level whilst sleeping in reality. Cobb and Adraine entered the limbo state to get Fischer out of there.
As Cobb was already in limbo state, there was no need for him to go to sleep there and dream.
You can also ask how could they go to sleep in turmoil in different levels. For your information, the PASIV has inbuilt arrangement to put sedatives into the user as per the requirement. You can look into this article for an insight into PASIV.
It is true that one needs to fall asleep in order to dream, and for such deep, consistent sleep the extractors use sedatives. But in the scene which you are referring, where Mal dies by Ariadne, Cobb never goes to sleep. He is able to deduce that Saito must be dead by now and floating in limbo. Thus he takes the leap from the building, so that he dies in that dream and he too enters limbo.
