I've never seen anything with both yeast and baking powder. What's the reason for that? Shouldn't e.g. muffins get even more fluffy by adding some yeast? Or bread by adding baking powder? I know there are differences in flavor, but there are cakes with yeast as also non-sweet things with baking powder. So that shouldn't be the problem...
The existing answers already explain why yeast and baking powder won't work together. But even if they did, you wouldn't have a reason to use them.
You seem to think that fluffiness depends on the amount of gas produced by the leaveners. In fact, it depends on both the gas and the ability of the dough to trap that gas. If you produce too much gas (no matter whether through yeast or through baking powder), then the fluffiness will be less than when using the optimal amount of leavener. This happens because your dough cannot hold the gas and the bubbles break, resulting in the dough deflating like a punctured tire. So even if combining two leaveners would have resulted in more "blowing big" action (which it doesn't, see the other answers), you would not end up with a fluffier end product. If you want fluffy muffins, you have to use a recipe and a technique which is best capable of retaining the gas produced by the baking powder. The amount of gas production is not a bottleneck.
Everything @Cascabel says in her answer is correct--I wanted to elaborate on why it is true.
In order for a yeast raised bread to work, since the yeast generates the raising gas (carbon dioxide) slowly over time, it has to stay trapped for a long time. This requires a good gluten network. The gluten network is like little rubber balloons throughout the dough, and the yeast blow them up with their.... erm... exhalations :-)
It takes a lot of work to blow up all the metaphorical gluten balloons, but the yeast is a slow and patient worker--it is like the turtle, not the hare. With patience you will get there.
Chemical leavenings like baking powder (or baking soda plus acid, which is what baking powder is) generate their gas quite quickly. They are normally used in batters that are going to go into the oven as soon as they are assembled (the famous muffin method), so that gluten does not develop, giving them their charactaristic tender crumb, unlike yeast raised bread.
If you establish the gluten network for slow yeast raising to work:
- You don't need the baking powder very much--you can (within reasonable limits) wait for the yeast to produce as much leavening as you desire.
- You have created a tough gluten network that the chemical leaveners, which are like sprinters, cannot raise very effectively. They just don't have the endurance to make it to the finish line. It is counter productive to add them, especially as they add a characteristic bitter or "chemical" taste for some people, or if there is too much.
There are some cases where you will see a small amount of baking soda (not powder) added to a yeast raised bread. One of my favorite toasting breads is in this category. The purpose of this baking soda is not to leaven, but rather to change the pH of the dough, making it less acidic, and facilitating browning of the crust.
As @Rumtscho has kindly pointed out is: If you did mix yeast and baking powder and then...
- ... wait a short time, then the yeast won't contribute any leavening (it will not start leavening soon enough)
- ... wait a long time, the baking powder won't contribute any leavening (it will spend itself before the dough goes into the oven)
Yeast raised breads are:
- Slower to create, as they require time for the yeast to work
- Have a yeasty flavor, which many people prize
- Require the gluten network of "balloons" to blow up, which lead to a chewy or toothsome bite to a greater or lesser extent
- Are not amenable to chemical leaveners which run out of oomph before the gluten network would be raised.
Chemically leavened quick breads are:
- Almost instant to rise--assemble the batter, and bake right away (with a few exceptions)
- No yeasty flavor
- No significant gluten network
- Much more tender crumb
- Some small risk of a chemical aftertaste if over leavened
You might want to have a read through Why use yeast instead of baking powder? to fully understand the differences between yeast and baking powder. The short summary is that baking powder tastes bad if there's enough to taste, but it's a lot easier and faster to use. But either one provides enough leavening to do pretty much whatever you want. Given that, the answer to your question is pretty much, why would you bother using both?
If you're okay with spending enough time to use yeast, you might as well use only yeast. Sure, maybe you could replace some of it with baking powder, but it won't save you any time, and it might taste worse. On the other hand, if you're okay with using just baking powder, why bother making your recipe take substantially longer? In either case, you'll be making things more complex without any real gain. If you want to make something fluffier, you can just increase the amount of the existing leavening; there's no need to combine two. And of course, in many cases, it's simply not feasible to use yeast. For example, a lot of quick breads (like muffins) are bad if overmixed, and letting them sit long enough for yeast to do its work would be bad too.
I think the case where you're thinking combined leavening would be useful is with something leavened with baking powder, where adding more would make it taste bad. But if it's possible to use yeast, then you might as well use only yeast. And if it's not feasible to use yeast, then maybe you use beaten egg whites to add fluff. Either way, you don't end up using a combination of yeast and baking powder.
There are of course breads leavened just with baking powder or baking soda (notably soda bread), and there are sweet baked goods leavened with yeast (for example cinnamon rolls). But in either case, there's really no reason to switch to using a combination of the two. Recipes pretty much pick the best tool for the job and go with it.
I have been using baking powder in yeast bread dough for a little while now. I dont use much, for about 3-4 cups of flour, I add maybe half a table spoon. The thing I have noticed what it does to the dough, is changes the density quite a bit. I had baked quite a bit of bread with just yeast, and no matter how long you let it rise, and rest, I was never able to get it as light of a consistency a with a little bit of baking powder.
Don't get me wrong, I don't advocate using it in all situations, as some breads are much better off with being baked without any baking powder at all, and will have a nicer flavor without it. But if you desire a nice light baguette for instance, or just a soft white bread, a small amount of baking powder will help with the texture quite a bit.
It will actually be very close in texture and taste to the type of baguette/white bread you get in the grocery store bakeries etc. It is quite tasty, and I would reccomend you try it if you want to experiment. Just remember, its not a great idea in all applications, some breads are really good when they are just a bit denser.
Actually I discovered many professional bakers do use small amounts of baking powder in their yeast breads. Some call it their secret. It is also used in packaged breads and acts as a dough improver for texture, not for more fluff. I add around 1/2 tsp baking powder to my pizza dough (around 2 1/2 - 3 cups flour) and it seems that it stretches easier. I also add to many bread recipes I have, 1/4 to 1/2 tsp. I do not know the science behind it but it works.
As far as adding yeast to muffins and cakes, I am not sure, but I have a couple recipes for sweets that includes semolina, and yeast along with baking powder is used. The cake has to rest an hour before baking even though it does not rise, but after baking, the texture is the desired one.