Another thing too is that the burden of proof is on the person claiming something from which there is no empirical evidence. In and of itself the burden of proof does not disprove the existence of a deity but it does get it off the atheists shoulders of having to disprove a claim posited by a theist.
So like in your unicorn example. It is not up to me to disprove that your invisible unicorn exists, it is up to you to prove to me that it does exist.