Rats that are separated long enough such that they can no longer make successful offspring have become two different species by the process of allopatric speciation. A species, by definition, is a group of individuals that can successfully interbreed, and a key factor to successful breeding is the viability of the offspring. If the rats cannot create healthy fertile offspring, then the rats are two different species.
In the real world, this process usually happens due to geographic separation; a great example is the Kaibab and Abert's squirrels, two different kinds of squirrels that were once the same species, until the Colorado River created the Grand Canyon and separated them into different populations, which are now recognized as different species. This link will take you to a lecture you can click through for more information and examples.