PhD in the wrong department?
Investigate with your potential advisor, director of graduate studies, or chair (in this order, for ease of everybody's life) the possibility of getting a co-advisor from the physics department, provided there is someone with an expertise on the topic. You may even look beyond your institution, but that would require some serious argument.

One of the comments to the question mentioned the issue of "labels" of degree. 
I don't see it being an issue for industry jobs. Many companies routinely hire physicists and computer scientists alike, and ask them to do similar jobs. 
If you want to get a faculty position in a physics department, then perhaps you may have an issue if you have a CS degree, but you may be able to play the game by publishing in both CS and physics venue.