If you want to teach a horse an abrupt stop, not just a slowing through 2 downward transitions, you have to set him up like a western horse and teach him to 'stop' rather than slow down until he is stopped. Are you riding English? If so, abrupt stops are not what English horses are supposed to do.
If you want an abrupt stop, you should first, collect the horse, get his hind end underneath him and get him to lift his belly and elevate his shoulders. Thus, you 'set him up' to stop on his hind end. An abrupt stop on a horse's front end is rough on both him and you, so you have to teach him to stop on his back end.
You need to collect him and get his shoulders up and keep him up in the bridle. Then, you form a barrier with your hands but YOU DO NOT PULL. Sit as if you are going to stop abruptly, quit riding the horse forward and say "Whoa!" If you have done your homework and gotten this horse up off of his front end, he will stop without you pulling on him. This is what I have always done with my 2 year olds and they will stop on their hind ends with no pull on their faces and even start taking a step or two with their front feet when they stop. I do not go fast enough to get a slide and do not put any sliders on them until they are 3, but they will all lock up when I say "Whoa!" and quit riding them forward.
I save saying the word "Whoa!" for hard stops only. But, any horse that has been taught to stop, will develop very light, non-resistant downward transitions just from having a rider quit riding them forward and sitting in a stopping position. The key is to get them collected, get them to shift their weight back and keep their shoulders elevated before you ask for a stop or a downward transition. Then and only then can they get off of their front ends and stop rather than have to pulled down to a slower speed and finally stop, with great resistance. When you pull a horse into a stop, he will learn to push on the reins and will job his front feet into the ground and it won't look pretty and it won't feel good. You cannot 'pull' a horse off of his front end. You have to 'push' his hind end under him so he can stop properly.